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Indefinite Integrals MATHS - Indefinite Integrals

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 732 questions in this chapter.

Question types

Indefinite Integrals question types

732 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

732
Questions
5
Question groups
5
Question types
Sample Questions

Indefinite Integrals questions

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

Q 1M.C.Q (1 Marks)1 Mark
$\int\text{x}\sec\text{x}^2\text{ dx}$ is equal to:
  1. $\frac{1}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  2. $\frac{\text{x}^2}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  3. $2\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  4. none of these.
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Q 2M.C.Q (1 Marks)1 Mark
The value of $\int\frac{1}{\text{x}+\text{x}\log\text{x}}\text{ dx}$ is:
  1. $1+\log\text{x}$
  2. $\text{x}+\log\text{x}$
  3. $\text{x}\log\text{x}(1+\log\text{x})$
  4. $\log(1+\log\text{x})$
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Q 3M.C.Q (1 Marks)1 Mark
$\int\frac{\text{x}+3}{(\text{x}+4)^2}\text{e}^{\text{x}}\text{ dx}=$
  1. $\frac{\text{e}^\text{x}}{\text{x}+4}+\text{C}$
  2. $\frac{\text{e}^\text{x}}{\text{x}+3}+\text{C}$
  3. $\frac{1}{(\text{x}+4)^2}+\text{C}$
  4. $\frac{\text{e}^\text{x}}{(\text{x}+4)^2}+\text{C}$
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Q 4M.C.Q (1 Marks)1 Mark
$\int\frac{1}{1-\cos\text{x}-\sin\text{x}}\text{ dx}=$
  1. $\log\big|1+\cot\frac{\pi}{2}\big|+\text{C}$
  2. $\log\big|1-\tan\frac{\pi}{2}\big|+\text{C}$
  3. $\log\big|1-\cot\frac{\pi}{2}\big|+\text{C}$
  4. $\log\big|1+\tan\frac{\pi}{2}\big|+\text{C}$
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Q 5M.C.Q (1 Marks)1 Mark
If $\int\frac{1}{(\text{x}+2)(\text{x}^2+1)}\text{ dx}=\text{a}\log|1+\text{x}^2|+\text{b}\tan^{-1}\text{x}+\frac{1}{5}\log|\text{x}+2|+\text{C},$ then
  1. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  2. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
  3. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  4. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
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