39. Choose the correct answer:

The area bounded by the y-axis, y = cos x and y = sin x when  0 ≤ x ≤ π/2.

(A) 2(√2 - 1)

(B) √2 - 1

(C) √2 + 1

(D) √2

Given curve is $y=cosx$

$y=sinx$ for $0\le x\le \frac{\pi }{2}$

And $y-axis$

We know that $sinx=cosx$ at $x=\frac{\pi }{4}and<\frac{\pi }{4}<\frac{\pi }{2}$ i.e,  $cos\frac{\pi }{4}=sin\frac{\pi }{4}=1/\surd 2$

So the point of intersection is at $x=\frac{\pi }{4}$

<p>Given curve is&nbsp;<math><mrow><mi>y</mi><mo>=</mo><mi>c</mi><mi>o</mi><mi>s</mi><mi>x</mi></mrow></math></p><p><math><mrow><mi>y</mi><mo>=</mo><mi>s</mi><mi>i</mi><mi>n</mi><mi>x</mi></mrow></math>&nbsp;for&nbsp;<math><mrow><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></p><p>And&nbsp;<math><mrow><mi>y</mi><mo>−</mo><mi>a</mi><mi>x</mi><mi>i</mi><mi>s</mi></mrow></math></p><p>We know that&nbsp;<math><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mi>x</mi><mo>=</mo><mi>c</mi><mi>o</mi><mi>s</mi><mi>x</mi></mrow></math>&nbsp;at&nbsp;<math><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mi>a</mi><mi>n</mi><mi>d</mi><mo>&lt;</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>&lt;</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math>&nbsp;i.e, &nbsp;<math><mi>c</mi><mi>o</mi><mi>s</mi><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mi>s</mi><mi>i</mi><mi>n</mi><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=1/√2</mo></math></p><p>So the point of intersection is at&nbsp;<math><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1742810483phpGTepV0_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1742810483phpGTepV0.jpeg" alt="" width="210" height="171"></picture></div><div><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1742810483phpGTepV0.jpeg"4 media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1742810546phpPqKVJK.jpeg" alt="" width="287" height="327"></picture></div></div></div></div>

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