Question

Match the following function in column I with their anti-derivatives in column II and choose the correct option from the codes given below.

Column I		Column II
A	$\cos x$	1	$-\cot x+C$
B	$\sin x$	2	$\sin x+C$
C	${\sec }^{2}x$	3	$-\cos x+C$
D	${\mathrm{cosec}}^{2}x$	4	$\tan x+C$

• A. A - (2), B - (3), C - (1), D - (4)
• B. A - (2), B - (3), C - (4), D - (1)
• C. A - (3), B - (2), C - (4), D - (1)
• D. A - (1), B - (2), C - (4), D - (3)

Answer 1

Answer: (B)

Derivatives		Anti - Derivatives
A	$\frac{d}{dx}(\sin x)=\cos x$;	$\int \cos xdx=\sin x+C$
B	$\frac{d}{dx}(-\cos x)=\sin x$;	$\int \sin xdx=-\cos x+C$
C	$\frac{d}{dx}(\tan x)={\sec }^{2}x$;	$\int {\sec }^{2}dx=\tan x+C$
D	$\frac{d}{dx}(-\cot x)={\mathrm{cosec}}^{2}x$;	$\int {\mathrm{cosec}}^{2}xdx=-\cot x+C$