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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
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.
$\frac{x}{2}+\frac{1}{4} \sin 2 x+C$
(A)
Let $I =\int \cos ^2 d x$
$
\begin{array}{l}
=\int \frac{1+\cos 2 x}{2} d x \\
=\frac{1}{2} x+\frac{1}{4} \sin 2 x+C
\end{array}
$
Hence option (A) is correct.

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