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Q.

The area between y = cotx and X-axis from $x = \frac{π}{4} to x = \frac{π}{2}$ is

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a

$2 \sqrt{2}$

b

log 2

c

$\log \sqrt{2}$

d

$\frac{π}{4}$

answer is B.

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Detailed Solution

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$Required area = \int_{\frac{π}{4}}^{\frac{π}{2}} cotx d x = {(\ln sinx)}_{\frac{π}{4}}^{\frac{π}{2}} = 0 - \ln \frac{1}{\sqrt{2}} = \ln \sqrt{2}$

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The area between y = cotx and X-axis from x=π4 to x=π2 is