CBSE Class 12 Maths Integrals Quiz 3

1. \(\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}\)

A 1 B 2 C \(\frac{π}{4}\) D \(\frac{π^2}{8}\)

2. \(\int_{0}^{\infty} \frac{1}{1+e^{x}}\) dx =

A log 2 B -log 2 C log 2 – 1 D log 4 – 1

3. \(\int_{0}^{1}\) x(1 – x) is equal to

A \(\frac{1}{10010}\) B \(\frac{1}{10100}\) C \(\frac{1}{1010}\) D \(\frac{11}{10100}\)

4. What is the value of \(\int_{0}^{1}\) \(\frac{d}{dx}\){sin(\(\frac{2x}{1+x^2}\))}dx?

A 0 B π C -π D \(\frac{π}{2}\)

5. \(\int_{0}^{1}\) \(\frac{x}{1+x}\) dx =

A 1 – log 2 B 2 C 1 + log 2 D log 2

6. ∫\(\frac{sin x + cos x}{\sqrt{1+2sin x}}\) dx =

A log(sin x – cos x) B x C log x D log sin (cos x)

7. ∫log xdx =

A log 10.x log(\(\frac{x}{e}\)) + c B log e.x log(\(\frac{x}{e}\)) + c C (x – 1) log x + c D \(\frac{1}{x}\) + c

8. ∫(\(\frac{cos 2θ – 1}{cos 2θ + 1}\)) dθ =

A tan θ – θ + c B θ + tan θ + c C θ – tan θ + c D -θ – cot θ + c

9. ∫\(\frac{2dx}{\sqrt{1-4x^2}}\) =

A tan (2x) + c B cot (2x) + c C cos(2x) + c D sin(2x) + c

10. Value of ∫\(\frac{dx}{\sqrt{2x – x^2}}\)

A sin(x – 1) + c B sin(1 + x) + c C sin(1 + x²) + c D –\(\sqrt{2x-x^2}\) + c