Question #65700

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Answer 1 · 2017-04-09T22:04:05

$pi/4$

$int_0^(pi/2)sin^2thetacolor(white).d theta$

Use the trigonometric identity $sin^2theta=1/2(1-cos2theta)$ :

$=1/2int_0^(pi/2)(1-cos2theta)d theta$

Integrating both terms separately:

$=1/2(theta-1/2sin2theta)|_0^(pi/2)$

Evaluating:

$=1/2[pi/2-1/2sinpi-(0-1/2sin0)]$

$=pi/4$