Q71 / 120 · VITEEE 2010 · Mathematics
The area bounded by the curve $y=|\sin x|, x$-axis and the lines $|x|=\pi$, is
- A$2 \mathrm{sq}$ unit
- B$1 \mathrm{sq}$ unit
- Correct answerC$4 \mathrm{sq}$ unit
- DNone of these
Solution
Required area = Shaded area
$$ \begin{array}{l} =\int_{-\pi}^{\pi}|\sin x| d x=2 \int_{0}^{\pi}|\sin x| d x \\ =-2[\cos x]_{0}^{\pi}=-2(\cos \pi-\cos 0) \\ =4 \text { squnits } \end{array} $$
$$ \begin{array}{l} =\int_{-\pi}^{\pi}|\sin x| d x=2 \int_{0}^{\pi}|\sin x| d x \\ =-2[\cos x]_{0}^{\pi}=-2(\cos \pi-\cos 0) \\ =4 \text { squnits } \end{array} $$
Hence, the correct answer is option: 'C'.