Question 1
Find the primitive of:
a) $2x$
a
$x^2+C$
Question ID: 50050010010
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b) $3x^2$
a
$x^3+C$
Question ID: 50050010020
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c) $7x^6$
a
$x^7+C$
Question ID: 50050010030
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d) $\frac32x^{\frac12}$
a
$x^{\frac32}+C$
Question ID: 50050010040
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e) $1.2x^{0.2}$
a
$x^{1.2}+C$
Question ID: 50050010050
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f) $-x^{-2}$
a
$x^{-1}+C$
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Question 2
Evaluate:
a) $\int 4x^3\,dx$
a
$x^4+C$
Question ID: 50050020010
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b) $\int 9x^8\,dx$
a
$x^9+C$
Question ID: 50050020020
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c) $\int -2x^{-3}\,dx$
a
$x^{-2}+C$
Question ID: 50050020030
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d) $\int \frac12x^{-\frac12}\,dx$
a
$x^{\frac12}+C$
Question ID: 50050020040
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Question 3
Evaluate:
a) $\int x\,dx$
a
$\frac12x^2+C$
Question ID: 50050030010
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b) $\int x^2\,dx$
a
$\frac13x^3+C$
Question ID: 50050030020
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c) $\int x^5\,dx$
a
$\frac16x^6+C$
Question ID: 50050030030
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d) $\int x^{-2}\,dx$
a
$-x^{-1}+C$
Question ID: 50050030040
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e) $\int x^{1.5}\,dx$
a
$0.4x^{2.5}+C$
Question ID: 50050030050
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f) $\int x^{\frac43}\,dx$
a
$\frac37x^{\frac73}+C$
Question ID: 50050030060
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g) $\int x^{\frac12}\,dx$
a
$\frac23x^{\frac32}+C$
Question ID: 50050030070
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h) $\int x^{\frac25}\,dx$
a
$\frac57x^{\frac75}+C$
Question ID: 50050030080
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Question 4
Evaluate:
a) $\int 8x\,dx$
a
$4x^2+C$
Question ID: 50050040010
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b) $\int 3x\,dx$
a
$\frac32x^2+C$
Question ID: 50050040020
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c) $\int 6x^2\,dx$
a
$2x^3+C$
Question ID: 50050040030
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d) $\int 4x^5\,dx$
a
$\frac23x^6+C$
Question ID: 50050040040
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e) $\int 9x^{17}\,dx$
a
$\frac12x^18+C$
Question ID: 50050040050
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f) $\int -2x^3\,dx$
a
$-\frac12x^4+C$
Question ID: 50050040060
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g) $\int -8x^{\frac12}\,dx$
a
$-\frac{16}{3}x^{\frac32}+C$
Question ID: 50050040070
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h) $\int -7x^{\frac34}\,dx$
a
$-4x^{\frac74}+C$
Question ID: 50050040080
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i) $\int \frac12x^7\,dx$
a
$\frac{1}{16}x^8+C$
Question ID: 50050040090
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j) $\int \frac65x^2\,dx$
a
$\frac25x^3+C$
Question ID: 50050040100
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k) $\int -\frac12x^-3\,dx$
a
$\frac14x^{-2}+C$
Question ID: 50050040110
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l) $\int -\frac97x^-5\,dx$
a
$\frac{9}{28}x^{-4}+C$
Question ID: 50050040120
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Question 5
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{1}^{2} x\,dx$
a
$\frac32$
Question ID: 50050050010
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b) $\int_{2}^{3} x^2\,dx$
a
$\frac{19}{3}$
Question ID: 50050050020
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c) $\int_{2}^{6} 4x^3\,dx$
a
$1280$
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d) $\int_{0}^{2} 2x^7\,dx$
a
$64$
Question ID: 50050050040
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e) $\int_{1}^{4} x^{\frac12}\,dx$
a
$\frac{14}{3}$
Question ID: 50050050050
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f) $\int_{3}^{5} x^{-2}\,dx$
a
$\frac{2}{15}$
Question ID: 50050050060
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g) $\int_{-1}^{1} \frac45x^{9}\,dx$
a
$0$
Question ID: 50050050070
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h) $\int_{-2}^{-1} -\frac32x^{-3}\,dx$
a
$\frac{9}{16}$
Question ID: 50050050080
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Question 6
Simplify and then evaluate:
a) $\int x\times x\,dx$
a
$\frac13x^3+C$
Question ID: 50050060010
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b) $\int (2x)^2\,dx$
a
$\frac43x^3+C$
Question ID: 50050060020
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c) $\int 4\times x\times x^2\,dx$
a
$x^4+C$
Question ID: 50050060030
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d) $\int \frac{1}{x^2}\,dx$
a
$-\frac{1}{x}+C$
Question ID: 50050060040
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e) $\int \frac{1}{x^4}\,dx$
a
$-\frac{1}{3x^3}+C$
Question ID: 50050060050
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f) $\int \frac{2}{x^2}\,dx$
a
$-\frac{2}{x}+C$
Question ID: 50050060060
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g) $\int \frac{3}{4x^5}\,dx$
a
$-\frac{3}{16x^4}+C$
Question ID: 50050060070
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h) $\int \frac{4}{x^8}\times\frac{2x^3}{5}\,dx$
a
$-\frac{2}{5x^4}+C$
Question ID: 50050060080
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Question 7
Evaluate. Leave answers as fractions where necessary.
a) $\int_{3}^{5} \frac{1}{x^2}\,dx$
a
$\frac{2}{15}$
Question ID: 50050070010
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b) $\int_{1}^{2} 3(2x)^2\,dx$
a
$28$
Question ID: 50050070020
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c) $\int_{-2}^{-1} \frac{3}{x^7}\,dx$
a
$-\frac{63}{128}$
Question ID: 50050070030
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d) $\int_{\frac14}^{\frac12} \left(\frac{4}{x^2}\right)\times\frac1x\,dx$
a
$24$
Question ID: 50050070040
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Question 8
Evaluate:
a) $\int \left(2x+3x^2\right)\,dx$
a
$x^2+x^3+C$
Question ID: 50050080010
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b) $\int \left(x+x^{-3}\right)\,dx$
a
$\frac12x^2-\frac12x^{-2}+C$
Question ID: 50050080020
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c) $\int \left(3x^5+2x^{\frac12}\right)\,dx$
a
$\frac12x^6+\frac43x^{\frac32}+C$
Question ID: 50050080030
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d) $\int \left(\frac{1}{x^3}+8x^{0.2}\right)\,dx$
a
$-\frac{1}{2x^2}+\frac{20}{3}x^{1.2}+C$
Question ID: 50050080040
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e) $\int \left(3x(1+4x)\right)\,dx$
a
$\frac32x^2+4x^3+C$
Question ID: 50050080050
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f) $\int \left(x+2\right)^2\,dx$
a
$\frac{x^3}{3}+2x^2+4x+C$
Question ID: 50050080060
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g) $\int 3\left(x+\frac1x\right)^2\,dx$
a
$x^3+6x-\frac3x+C$
Question ID: 50050080070
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h) $\int \left(2x\left(2x+1\right)^2+\frac1x\times\frac4x\right)\,dx$
a
$2x^4+\frac83x^3+x^2-\frac4x+C$
Question ID: 50050080080
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Question 9
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{0}^{\frac12} \left(x^5+16x\right)\,dx$
a
$\frac{49}{24}$
Question ID: 50050090010
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b) $\int_{1}^{2} \left(3x^2-x^{-2}\right)\,dx$
a
$\frac{13}{2}$
Question ID: 50050090020
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c) $\int_{-1}^{0} \left(3-x\right)^2\,dx$
a
$\frac{37}{3}$
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d) $\int_{1}^{6} 2\left(\frac3x+x^2\right)^2\,dx$
a
$3335$
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Question 10
Evaluate:
a) $\int \frac{2x+x^2}{x}\,dx$
a
$2x+\frac12x^2+C$
Question ID: 50050100010
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b) $\int \frac{x+9}{\sqrt x}\,dx$
a
$\frac23x^{\frac32}+18\sqrt x+C$
Question ID: 50050100020
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c) $\int \frac{(2x^2+5x)^2}{3x}\,dx$
a
$\frac13x^4+\frac{20}{9}x^3+\frac{25}{6}x^2+C$
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Question 11
Find the value of $a$ given that:
a) $\int_{a}^{2} x^3\,dx=\frac{15}{4}$
a
$a=1$
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b) $\int_{0}^{a} (3x-2)^2\,dx=245$
a
$a=5$
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c) $\int_{4}^{9} a\sqrt{x}\,dx=\frac{76}{3}$
a
$a=2$
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Question 1
Find the primitive of:
a) $2x$
b) $3x^2$
c) $7x^6$
d) $\frac32x^{\frac12}$
e) $1.2x^{0.2}$
f) $-x^{-2}$
Question 2
Evaluate:
a) $\int 4x^3\,dx$
b) $\int 9x^8\,dx$
c) $\int -2x^{-3}\,dx$
d) $\int \frac12x^{-\frac12}\,dx$
Question 3
Evaluate:
a) $\int x\,dx$
b) $\int x^2\,dx$
c) $\int x^5\,dx$
d) $\int x^{-2}\,dx$
e) $\int x^{1.5}\,dx$
f) $\int x^{\frac43}\,dx$
g) $\int x^{\frac12}\,dx$
h) $\int x^{\frac25}\,dx$
Question 4
Evaluate:
a) $\int 8x\,dx$
b) $\int 3x\,dx$
c) $\int 6x^2\,dx$
d) $\int 4x^5\,dx$
e) $\int 9x^{17}\,dx$
f) $\int -2x^3\,dx$
g) $\int -8x^{\frac12}\,dx$
h) $\int -7x^{\frac34}\,dx$
i) $\int \frac12x^7\,dx$
j) $\int \frac65x^2\,dx$
k) $\int -\frac12x^-3\,dx$
l) $\int -\frac97x^-5\,dx$
Question 5
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{1}^{2} x\,dx$
b) $\int_{2}^{3} x^2\,dx$
c) $\int_{2}^{6} 4x^3\,dx$
d) $\int_{0}^{2} 2x^7\,dx$
e) $\int_{1}^{4} x^{\frac12}\,dx$
f) $\int_{3}^{5} x^{-2}\,dx$
g) $\int_{-1}^{1} \frac45x^{9}\,dx$
h) $\int_{-2}^{-1} -\frac32x^{-3}\,dx$
Question 6
Simplify and then evaluate:
a) $\int x\times x\,dx$
b) $\int (2x)^2\,dx$
c) $\int 4\times x\times x^2\,dx$
d) $\int \frac{1}{x^2}\,dx$
e) $\int \frac{1}{x^4}\,dx$
f) $\int \frac{2}{x^2}\,dx$
g) $\int \frac{3}{4x^5}\,dx$
h) $\int \frac{4}{x^8}\times\frac{2x^3}{5}\,dx$
Question 7
Evaluate. Leave answers as fractions where necessary.
a) $\int_{3}^{5} \frac{1}{x^2}\,dx$
b) $\int_{1}^{2} 3(2x)^2\,dx$
c) $\int_{-2}^{-1} \frac{3}{x^7}\,dx$
d) $\int_{\frac14}^{\frac12} \left(\frac{4}{x^2}\right)\times\frac1x\,dx$
Question 8
Evaluate:
a) $\int \left(2x+3x^2\right)\,dx$
b) $\int \left(x+x^{-3}\right)\,dx$
c) $\int \left(3x^5+2x^{\frac12}\right)\,dx$
d) $\int \left(\frac{1}{x^3}+8x^{0.2}\right)\,dx$
e) $\int \left(3x(1+4x)\right)\,dx$
f) $\int \left(x+2\right)^2\,dx$
g) $\int 3\left(x+\frac1x\right)^2\,dx$
h) $\int \left(2x\left(2x+1\right)^2+\frac1x\times\frac4x\right)\,dx$
Question 9
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{0}^{\frac12} \left(x^5+16x\right)\,dx$
b) $\int_{1}^{2} \left(3x^2-x^{-2}\right)\,dx$
c) $\int_{-1}^{0} \left(3-x\right)^2\,dx$
d) $\int_{1}^{6} 2\left(\frac3x+x^2\right)^2\,dx$
Question 10
Evaluate:
a) $\int \frac{2x+x^2}{x}\,dx$
b) $\int \frac{x+9}{\sqrt x}\,dx$
c) $\int \frac{(2x^2+5x)^2}{3x}\,dx$
Question 11
Find the value of $a$ given that:
a) $\int_{a}^{2} x^3\,dx=\frac{15}{4}$
b) $\int_{0}^{a} (3x-2)^2\,dx=245$
c) $\int_{4}^{9} a\sqrt{x}\,dx=\frac{76}{3}$
Question 1
Find the primitive of:
a) $2x$
b) $3x^2$
c) $7x^6$
d) $\frac32x^{\frac12}$
e) $1.2x^{0.2}$
f) $-x^{-2}$
Question 2
Evaluate:
a) $\int 4x^3\,dx$
b) $\int 9x^8\,dx$
c) $\int -2x^{-3}\,dx$
d) $\int \frac12x^{-\frac12}\,dx$
Question 3
Evaluate:
a) $\int x\,dx$
b) $\int x^2\,dx$
c) $\int x^5\,dx$
d) $\int x^{-2}\,dx$
e) $\int x^{1.5}\,dx$
f) $\int x^{\frac43}\,dx$
g) $\int x^{\frac12}\,dx$
h) $\int x^{\frac25}\,dx$
Question 4
Evaluate:
a) $\int 8x\,dx$
b) $\int 3x\,dx$
c) $\int 6x^2\,dx$
d) $\int 4x^5\,dx$
e) $\int 9x^{17}\,dx$
f) $\int -2x^3\,dx$
g) $\int -8x^{\frac12}\,dx$
h) $\int -7x^{\frac34}\,dx$
i) $\int \frac12x^7\,dx$
j) $\int \frac65x^2\,dx$
k) $\int -\frac12x^-3\,dx$
l) $\int -\frac97x^-5\,dx$
Question 5
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{1}^{2} x\,dx$
b) $\int_{2}^{3} x^2\,dx$
c) $\int_{2}^{6} 4x^3\,dx$
d) $\int_{0}^{2} 2x^7\,dx$
e) $\int_{1}^{4} x^{\frac12}\,dx$
f) $\int_{3}^{5} x^{-2}\,dx$
g) $\int_{-1}^{1} \frac45x^{9}\,dx$
h) $\int_{-2}^{-1} -\frac32x^{-3}\,dx$
Question 6
Simplify and then evaluate:
a) $\int x\times x\,dx$
b) $\int (2x)^2\,dx$
c) $\int 4\times x\times x^2\,dx$
d) $\int \frac{1}{x^2}\,dx$
e) $\int \frac{1}{x^4}\,dx$
f) $\int \frac{2}{x^2}\,dx$
g) $\int \frac{3}{4x^5}\,dx$
h) $\int \frac{4}{x^8}\times\frac{2x^3}{5}\,dx$
Question 7
Evaluate. Leave answers as fractions where necessary.
a) $\int_{3}^{5} \frac{1}{x^2}\,dx$
b) $\int_{1}^{2} 3(2x)^2\,dx$
c) $\int_{-2}^{-1} \frac{3}{x^7}\,dx$
d) $\int_{\frac14}^{\frac12} \left(\frac{4}{x^2}\right)\times\frac1x\,dx$
Question 8
Evaluate:
a) $\int \left(2x+3x^2\right)\,dx$
b) $\int \left(x+x^{-3}\right)\,dx$
c) $\int \left(3x^5+2x^{\frac12}\right)\,dx$
d) $\int \left(\frac{1}{x^3}+8x^{0.2}\right)\,dx$
e) $\int \left(3x(1+4x)\right)\,dx$
f) $\int \left(x+2\right)^2\,dx$
g) $\int 3\left(x+\frac1x\right)^2\,dx$
h) $\int \left(2x\left(2x+1\right)^2+\frac1x\times\frac4x\right)\,dx$
Question 9
Evaluate. Leave answers as improper fractions where necessary.
a) $\int_{0}^{\frac12} \left(x^5+16x\right)\,dx$
b) $\int_{1}^{2} \left(3x^2-x^{-2}\right)\,dx$
c) $\int_{-1}^{0} \left(3-x\right)^2\,dx$
d) $\int_{1}^{6} 2\left(\frac3x+x^2\right)^2\,dx$
Question 10
Evaluate:
a) $\int \frac{2x+x^2}{x}\,dx$
b) $\int \frac{x+9}{\sqrt x}\,dx$
c) $\int \frac{(2x^2+5x)^2}{3x}\,dx$
Question 11
Find the value of $a$ given that:
a) $\int_{a}^{2} x^3\,dx=\frac{15}{4}$
b) $\int_{0}^{a} (3x-2)^2\,dx=245$
c) $\int_{4}^{9} a\sqrt{x}\,dx=\frac{76}{3}$
Answers
Question 1
a) $x^2+C$
b) $x^3+C$
c) $x^7+C$
d) $x^{\frac32}+C$
e) $x^{1.2}+C$
f) $x^{-1}+C$
Question 2
a) $x^4+C$
b) $x^9+C$
c) $x^{-2}+C$
d) $x^{\frac12}+C$
Question 3
a) $\frac12x^2+C$
b) $\frac13x^3+C$
c) $\frac16x^6+C$
d) $-x^{-1}+C$
e) $0.4x^{2.5}+C$
f) $\frac37x^{\frac73}+C$
g) $\frac23x^{\frac32}+C$
h) $\frac57x^{\frac75}+C$
Question 4
a) $4x^2+C$
b) $\frac32x^2+C$
c) $2x^3+C$
d) $\frac23x^6+C$
e) $\frac12x^18+C$
f) $-\frac12x^4+C$
g) $-\frac{16}{3}x^{\frac32}+C$
h) $-4x^{\frac74}+C$
i) $\frac{1}{16}x^8+C$
j) $\frac25x^3+C$
k) $\frac14x^{-2}+C$
l) $\frac{9}{28}x^{-4}+C$
Question 5
a) $\frac32$
b) $\frac{19}{3}$
c) $1280$
d) $64$
e) $\frac{14}{3}$
f) $\frac{2}{15}$
g) $0$
h) $\frac{9}{16}$
Question 6
a) $\frac13x^3+C$
b) $\frac43x^3+C$
c) $x^4+C$
d) $-\frac{1}{x}+C$
e) $-\frac{1}{3x^3}+C$
f) $-\frac{2}{x}+C$
g) $-\frac{3}{16x^4}+C$
h) $-\frac{2}{5x^4}+C$
Question 7
a) $\frac{2}{15}$
b) $28$
c) $-\frac{63}{128}$
d) $24$
Question 8
a) $x^2+x^3+C$
b) $\frac12x^2-\frac12x^{-2}+C$
c) $\frac12x^6+\frac43x^{\frac32}+C$
d) $-\frac{1}{2x^2}+\frac{20}{3}x^{1.2}+C$
e) $\frac32x^2+4x^3+C$
f) $\frac{x^3}{3}+2x^2+4x+C$
g) $x^3+6x-\frac3x+C$
h) $2x^4+\frac83x^3+x^2-\frac4x+C$
Question 9
a) $\frac{49}{24}$
b) $\frac{13}{2}$
c) $\frac{37}{3}$
d) $3335$
Question 10
a) $2x+\frac12x^2+C$
b) $\frac23x^{\frac32}+18\sqrt x+C$
c) $\frac13x^4+\frac{20}{9}x^3+\frac{25}{6}x^2+C$
Question 11
a) $a=1$
b) $a=5$
c) $a=2$