KCET · Maths · Ellipse
Area of the region bounded by the curve \( y=\cos x, x=0 \) and \( x=\pi \) is
- A \( 2 \) sq. units
- B \( 4 \) sq. units
- C \( 3 \) sq. units
- D \( 1 \) sq. units
Answer & Solution
Correct Answer
(A) \( 2 \) sq. units
Step-by-step Solution
Detailed explanation
Given that, \( y=\cos x \rightarrow(1) \)
So, required area is given by \( \int_{0}^{\pi} \cos x d x=2 \int_{0}^{\frac{\pi}{2}} \cos x d x \)
\[
\begin{array}{l}
=\left.2(\sin x)\right|_{0} ^{\frac{\pi}{2}} \\
=2\left[\sin \frac{\pi}{2}-\sin 0\right]=2 \times 1=2 s q . \text { units }
\end{array}
\]
So, required area is given by \( \int_{0}^{\pi} \cos x d x=2 \int_{0}^{\frac{\pi}{2}} \cos x d x \)
\[
\begin{array}{l}
=\left.2(\sin x)\right|_{0} ^{\frac{\pi}{2}} \\
=2\left[\sin \frac{\pi}{2}-\sin 0\right]=2 \times 1=2 s q . \text { units }
\end{array}
\]
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