Match List-I with List-II

Choose the correct answer from the options given below :

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

The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

(A) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}\sin^5xdx=0$ (IV) odd function

(B) $\int\limits^{\frac{\pi }{2}}_{-\frac{\pi }{2}}(x^3+\tan^3x+1)dx=0+0+\left(\frac{\pi }{2}+\frac{\pi }{2}\right)=\pi$ (I)

(C) $I=\int\limits^{\frac{\pi }{2}}_{0}\frac{\cos^5x}{\cos^5x+\sin^5x}dx$

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

(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)