. Applied calculus; principles and applications . area Z^BC = area ZBC J\dz\ where a; = x = a cos 6, and z = ad cos 6d (ad) = a? sin Q I=«- Example 9. Given a right cyUnderof altitude h, and radius of base a diameter of the upper basetwo planes are passed, touching the lower base on opposite sides. Find the volume included between the planes. 280 INTEGRAL CALCULUS y = r A, dx = 4 r {MNPR) dx = 4: tyz dx t/O t/O Jo = 4 r(a-x)^^ia-x)dxJo a^ = — pa (a2 - x^)-^ dx-— r (a2 - x^)^ x dxa Jo a Jo [_Z Ji ajo o tt Jo TTO^h— 5 a2/i= (vol, of cylinder) — (vol. outside the planes). Here OA MN = R

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. Applied calculus; principles and applications . area Z^BC = area ZBC J\dz\ where a; = x = a cos 6, and z = ad cos 6d (ad) = a? sin Q I=«- Example 9. Given a right cyUnderof altitude h, and radius of base a diameter of the upper basetwo planes are passed, touching the lower base on opposite sides. Find the volume included between the planes. 280 INTEGRAL CALCULUS y = r A, dx = 4 r {MNPR) dx = 4: tyz dx t/O t/O Jo = 4 r(a-x)^^ia-x)dxJo a^ = — pa (a2 - x^)-^ dx-— r (a2 - x^)^ x dxa Jo a Jo [_Z Ji ajo o tt Jo TTO^h— 5 a2/i= (vol, of cylinder) — (vol. outside the planes). Here OA MN = RP = y = (a - x^)^. lY NP = z = -{a-x);

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