KCET · Maths · Area Under Curves
The area of the region bounded by \( y \)-axis. \( y=\cos x \) and \( y=\sin x ; 0 \leq x \leq \frac{\pi}{2} \) is
- A \( \sqrt{2} \) Sq.units
- B \( 2-\sqrt{2} \) Sq.units
- C \( \sqrt{2}-1 \) Sq.units
- D \( \sqrt{2}+1 \) Sq.units
Answer & Solution
Correct Answer
(C) \( \sqrt{2}-1 \) Sq.units
Step-by-step Solution
Detailed explanation
\[
\begin{array}{l}
\text { Required area }=\int_{0}^{\frac{\pi}{4}}(\cos x-\sin x) d x \\
=(\sin x+\cos x)_{0}^{\frac{\pi}{4}} \\
=\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1\right) \\
=(\sqrt{2}-1) \text { sq units }
\end{array}
\]
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