9. + 1.6 points My Notes Ask Your Teache Show Ouestion Details Jnded by y - sin

Question

9. + 1.6 points My Notes Ask Your Teache Show Ouestion Details Jnded by y - sin x and the x-axis on the interval [0, t/2]. Write a definite integral for the volume V of the solid formed when R is revolved around the x- al, aiIULIICI I 1111u . Type pi for if needed in the integral limits. rval [0, /2]. 1- v= symbolic formatting help 10. + 1 points My Notes Ask Your Teache Evaluate the following integral by first finding the antiderivative and then evaluating (exact value) 0 dt 4 V64 - 2 symbolic fotmatting help symbolic formatting help

Explanation / Answer

9)given curve is y =sinx , 0<=x<=/2

radius =sinx

volume by washer method v =[0 to /2](sinx)2 dx

v =[0 to /2](1-cos2x)/2 dx

v =(/2)[0 to /2] (1-cos2x)dx

v =(/2)[0 to /2] (x-(1/2)sin2x)

v =(/2)((/2)-(1/2)sin2(/2)) -(/2)(0-(1/2)sin0)

v =(/2)((/2)-(1/2)sin) -(/2)(0-0)

v =(/2)((/2)-0) -0

v =2/4

volume =2/4=2.4674cubic units

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