^2 d x का मान है- - Vidyadip

MCQ

$\int \cos ^2 d x$ का मान है-

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

(A) $\frac{x}{2}+\frac{1}{4} \sin 2 x+C$
माना $I =\int \cos ^2 d x$
$\quad$$\quad$$=\int \frac{1+\cos 2 x}{2} d x$
$\quad$$\quad$$=\frac{1}{2} x+\frac{1}{4} \sin 2 x+C$
अत: सही विकल्प (A) है।

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