Question types

Definite Integrals question types

345 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

345
Questions
4
Question groups
5
Question types
Sample Questions

Definite Integrals questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

$\int\limits^1_0\frac{\text{d}}{\text{dx}}\Big\{\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)\Big\}\text{dx}$ is equal to:

  1. $0$

  2. ${\pi}$

  3. $\frac{\pi}{2}$

  4. $\frac{\pi}{4}$

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$\int\limits^3_0\frac{3\text{x}+1}{\text{x}^2+9}\text{ dx}=$

  1. $\frac{\pi}{12}+\log\big(2\sqrt{2}\big)$

  2. $\frac{\pi}{2}+\log\big(2\sqrt{2}\big)$

  3. $\frac{\pi}{6}+\log\big(2\sqrt{2}\big)$

  4. $\frac{\pi}{3}+\log\big(2\sqrt{2}\big)$

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Q 82 Marks2 Marks
Evaluate the following definite integrals:
$\int_{-2}\limits^{\frac{1}{2}}\frac{1}{\sqrt{1-\text{x}^2}} \text{ dx}$
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Q 92 Marks2 Marks
Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\log\Big(\frac{\text{a}-\sin\theta}{\text{a}+\sin\theta}\Big)\text{d}\theta$
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Q 102 Marks2 Marks
Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\text{x}\cos^2\text{x}\text{ dx}$
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Q 113 Marks3 Marks
Evaluate the following integrals:
$\int_{0}^\limits{1}\frac{\sqrt{\tan^{-1}\text{x}}}{1+\text{x}^2}\text{ dx}$
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Q 184 Marks4 Marks
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}}\frac{\cos^{2}\text{x}}{1+\text{e}^{\text{x}}}\text{ dx}$
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Q 194 Marks4 Marks
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}}\frac{\tan^{2}\text{x}}{1+\text{e}^{\text{x}}}\text{ dx}$
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Q 204 Marks4 Marks
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}}\frac{\text{x}^{11}-3\text{x}^9+5\text{x}^7-\text{x}^5+1}{\cos^2\text{x}}\text{ dx}$
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