Integrals — Course Quiz | Expresswala Academy

Ten questions on indefinite integrals, special methods and definite integrals. Pick one answer for each.

10 questions, one mark each. 6 to pass. Suggested time: 20 minutes. Your answers are not recorded.

$\displaystyle\int\frac{1}{x}\,dx$ equals

A $\displaystyle -\dfrac{1}{x^2} + C$

B $\log\lvert x \rvert + C$

C $\displaystyle \dfrac{1}{x^2} + C$

D $x\log x + C$
$\displaystyle\int\sec^2 x\,dx$ equals

A $\tan x + C$

B $-\cot x + C$

C $\displaystyle \dfrac{\sec^3 x}{3} + C$

D $\sec x + C$
$\displaystyle\int\sqrt{x}\,dx$ equals

A $\displaystyle \tfrac{2}{3}x^{1/2} + C$

B $\displaystyle \tfrac{2}{3}x^{3/2} + C$

C $\displaystyle \tfrac{1}{2\sqrt{x}} + C$

D $\displaystyle \tfrac{3}{2}x^{3/2} + C$
$\displaystyle\int e^{3x}\,dx$ equals

A $\displaystyle \dfrac{e^{3x + 1}}{3x + 1} + C$

B $e^{3x} + C$

C $\displaystyle \dfrac{e^{3x}}{3} + C$

D $3e^{3x} + C$
$\displaystyle\int\frac{\log x}{x}\,dx$ equals

A $(\log x)^2 + C$

B $\log(\log x) + C$

C $\displaystyle \dfrac{(\log x)^2}{2} + C$

D $\displaystyle \dfrac{\log x}{x^2} + C$
$\displaystyle\int\frac{dx}{x^2 + 2x + 5}$ equals

A $\displaystyle \tan^{-1}\dfrac{x + 1}{2} + C$

B $\displaystyle \dfrac{1}{2}\tan^{-1}\dfrac{x + 1}{2} + C$

C $\displaystyle \dfrac{1}{2}\tan^{-1}\dfrac{x + 2}{2} + C$

D $\displaystyle \dfrac{1}{4}\tan^{-1}\dfrac{x + 1}{4} + C$
$\displaystyle\int x\cos x\,dx$ equals

A $\displaystyle \dfrac{x^2}{2}\sin x + C$

B $-x\sin x + \cos x + C$

C $x\sin x + \cos x + C$

D $x\sin x - \cos x + C$
Evaluate $\displaystyle\int_1^2\frac{dx}{x}$ .

A $1$

B $\log 2$

C $\displaystyle -\tfrac{1}{2}$

D $\displaystyle \tfrac{1}{2}$
Evaluate $\displaystyle\int_0^{\pi}\sin x\,dx$ .

A $1$

B $-2$

C $2$

D $0$
Evaluate $\displaystyle\int_0^3\lvert x - 1 \rvert\,dx$ .

A $\displaystyle \tfrac{1}{2}$

B $\displaystyle \tfrac{5}{2}$

C $\displaystyle \tfrac{3}{2}$

D $2$

Unanswered questions are marked wrong.

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Integrals — Course Quiz

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