Match List-I woth List-II

Choose the correct answer from the options given below :

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

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

(A) $\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}sin^7x\, dx=0$ (III)

(B) $\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}(x\, \cos x+1)dx$

(C) $\int\limits^{\frac{\pi}{2}}_{0}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$ ...(1)

$\int\limits^{\frac{\pi}{2}}_{0}\frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$ ...(2)

$⇒2I=\int\limits^{\frac{\pi}{2}}_{0}1dx⇒I=\frac{\pi}{4}$ (IV)

(D) $\int\limits^{\sqrt{3}}_{1}\frac{dx}{1+x^2}=\left[\tan^{-1}x\right]^{\sqrt{3}}_{1}=\frac{\pi}{3}-\frac{\pi}{4}=\frac{\pi}{12}$ (II)