CBSE Class 12 Maths Integrals Quiz 4

1. ∫x² sin x³ dx =

A \(\frac{1}{3}\) cos x³ + c B –\(\frac{1}{3}\) cos x + c C \(\frac{-1}{3}\) cos x³ + c D \(\frac{1}{2}\) sin² x³ + c

2. ∫\(\frac{cos 2x- cos 2θ}{cos x – cos θ}\)dx is equal to

A 2 (sin x + x cos θ) + C B 2 (sin x – x cos θ) + C C 2 (sin x + 2x cos θ) + C D 2 (sin x – 2x cos θ) + C

3. ∫\(\frac{dx}{sin(x-a)sin(x-b)}\) is equal to

A sin(b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C B cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-b)}\)| + C C cosec (b – a) log |\(\frac{sin (x-b)}{sin(x-a)}\)| + C D sin (b – a) log |\(\frac{sin (x-a)}{sin(x-b)}\)| + C

4. ∫tan √xdx is equal to

A (x + 1)tan √x – √x + C B x tan √x – √x + C C √x – x tan √x + C D √x – (x + 1)tan √x + C

5. ∫e(\(\frac{1-x}{1+x^2}\))² dx is equal to

A \(\frac{e^x}{1+x^2}\) + C B –\(\frac{-e^x}{1+x^2}\) + C C \(\frac{e^x}{(1+x^2)^2}\) + C D \(\frac{-e^x}{(1+x^2)^2}\) + C

6. If ∫\(\frac{dx}{(x+2)(x^2+1)}\) = a log |1 + x²| + b tan x + \(\frac{1}{5}\) log |x + 2| + C, then

A a = \(\frac{-1}{10}\), b = \(\frac{-2}{5}\) B a = \(\frac{1}{10}\), b = \(\frac{-2}{5}\) C a = \(\frac{-1}{10}\), b = \(\frac{2}{5}\) D a = \(\frac{1}{10}\), b = \(\frac{2}{5}\)

7. ∫ \(\frac{x^3}{x+1}\) is equal to

A x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 – x| + C B x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 – x| + C C x + \(\frac{x^2}{2}\) – \(\frac{x^3}{3}\) – log |1 + x| + C D x + \(\frac{x^2}{2}\) + \(\frac{x^3}{3}\) – log |1 + x| + C

8. If ∫\(\frac{x^3dx}{\sqrt{1+x^2}}\) = a(1 + x²)+ b\(\sqrt{1 + x^2}\) + C, then

A a = \(\frac{1}{3}\), b = 1 B a = \(\frac{-1}{3}\), b = 1 C a = \(\frac{-1}{3}\), b = -1 D a = \(\frac{1}{3}\), b = -1

9. \(\int_{-\pi / 4}^{\pi / 4}\) \(\frac{dx}{1+cos 2x}\) dx is equal to

A 1 B 2 C 3 D 4

10. \(\int_{0}^{\pi / 2}\) \(\sqrt{1+sin 2x}\) dx is equal to

A 2√2 B 2(√2 + 1) C 0 D 2(√2 – 1)