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  • Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 28 maths

Explain solution RD Sharma class 12 chapter 20 Areas of Bounded Regions exercise multiple choice question 28 maths

Answers (1)

Answer:

 (b)

Hint:

 Integration

Given:

 y=cos\, x, y=sin\, x,0\leq x\leq \frac{\pi }{2}

Explanation:

Intersection point,

\begin{aligned} &cos\, x=sin\, x\\ &-tan\, x=1\\ &x=\frac{\pi }{4}, 0\leq x\leq \frac{\pi }{2} \end{aligned}

Area AOB

\begin{aligned} &=\int_{0}^{\frac{\pi }{4}}(cos\, x-sin\, \, x)dx\\ &=\left [ sin\, x+cos\, x \right ]_{0}^{\frac{\pi }{4}}\\ &=sin\frac{\pi }{4}-sin\, 0+cos\frac{\pi }{4}-cos\, 0\\ &=\frac{1}{\sqrt{2}}+0+\frac{1}{\sqrt{2}}-1\\ &=-1+\frac{2}{\sqrt{2}}\\ &=-1+\sqrt{2}\\ &=\sqrt{2}-1 \end{aligned}

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Gurleen Kaur

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