^2 d x is equal to: - Vidyadip

MCQ

$\int \cos ^2 d x$ is equal to:

✓
$\frac{x}{2}+\frac{1}{4} \sin 2 x+C$
B
$x^2+\frac{1}{4} \sin 2 x+ C$
C
$\frac{x}{4}+\frac{1}{2} \sin x+C$
D
$\frac{x^2}{2}+\frac{1}{2} \sin ^2 x+ C$

✓

Answer

Correct option: A.

$\frac{x}{2}+\frac{1}{4} \sin 2 x+C$

Let $I =\int \cos ^2 d x$
$=\int \frac{1+\cos 2 x}{2} d x$
$=\frac{1}{2} x+\frac{1}{4} \sin 2 x+C$
Hence option (A) is correct.

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