Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

Match List-I with List-II.

List-I List-II
(A) $\int\limits^{1}_{-1}|x|dx$ (I) 0
(B) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}sinx\,  dx$ (II) 2
(C) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}cos x\,  dx$ (III) $\frac{\pi }{4}$
(D) $\int\limits^{\frac{\pi }{2}}_{0}sin^2x\,  dx$ (IV) 1

Choose the correct option from the ones given below :

Options:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A)-(I), (B)-(IV), (C)-(II), (D)-(III)

(A)-(IV), (B)-(I), (C)-(III), (D)-(II)

Correct Answer:

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

Explanation:

The correct answer is Option (2) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

(A) $\int\limits^{1}_{-1}|x|dx=2\int\limits_0^1x\,dx=1$ (IV)

(B) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}\sin x\,  dx=0$ (Odd function) (I)

(C) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}\cos x\,  dx=\left[\sin x\right]^{\frac{\pi }{2}}_{-\frac{\pi }{2}}=2$ (II)

(D) $\int\limits^{\frac{\pi }{2}}_{0}\sin^2x\,  dx=\int\limits^{\frac{\pi }{2}}_{0}\frac{1-\cos 2x}{2}dx=\frac{\pi}{4}$ (III)