MCQ
Area bounded by the curve $y=\cos x$ between $x=0$ and $x=\frac{3 \pi}{2}$ is
- A1 sq. unit
- B2 sq. units
- ✓3 sq. units
- D4 sq. units
✓
Answer
Correct option: C.
3 sq. units
(c): We have, $y=\cos x$, whose graph is shown below, between $x=0$ and $x=\frac{3 \pi}{2}$
$\therefore \quad$ Required area
$
\begin{array}{l}
=\int_0^{\pi / 2} \cos x d x+\left|\int_{\pi / 2}^{3 \pi / 2} \cos x d x\right| \\
=[\sin x]_0^{\pi / 2}+\left|[\sin x]_{\pi / 2}^{3 \pi / 2}\right| \\
=1+|(-1-1)|=1+2=3 \text { sq. units }
\end{array}
$
$\therefore \quad$ Required area
$
\begin{array}{l}
=\int_0^{\pi / 2} \cos x d x+\left|\int_{\pi / 2}^{3 \pi / 2} \cos x d x\right| \\
=[\sin x]_0^{\pi / 2}+\left|[\sin x]_{\pi / 2}^{3 \pi / 2}\right| \\
=1+|(-1-1)|=1+2=3 \text { sq. units }
\end{array}
$
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