The function B(a, B) is defined by a-'(1 – y)"-'dy. (a) Letting y = sin² 0 show that B(a, B) = 2 fo/2 sin² 2a-1 cos-1 d0. (b) Write r(a)r(B) as a double integral, transform to polar coordinates, and conclude that B(a, ß) Га+)

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The function B(a, B) is defined by
(a) Letting y = sin² Ø show that B(a, B) = 2 /2 sin2a-1 cos²8-1 d0.
(b) Write r(a)r (ß) as a double integral, transform to polar coordinates, and conclude that B(a, ß)
r(a)r()
T(a+8)
Transcribed Image Text:The function B(a, B) is defined by (a) Letting y = sin² Ø show that B(a, B) = 2 /2 sin2a-1 cos²8-1 d0. (b) Write r(a)r (ß) as a double integral, transform to polar coordinates, and conclude that B(a, ß) r(a)r() T(a+8)
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