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Evaluate : int_(0)^(a)x^(5//2)sqrt(a-x)dx |
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Answer» Solution :`{:("Put" x = a sin^(2)theta,rArr,dx=2asinthetacostheta d theta),("Lower LIMIT" : x = 0, rArr, theta = 0),("Upper limit" x = a , rArr, theta = pi/2):}` `underset(0)OVERSET(pi)intx^(5//2)SQRT(a-x)dx=underset(0)overset(pi/2)int2a^(4)sin^(6)theta d theta = 2a^(4) xx (pi)/(2).((5.31)(1))/(8.64.2) = (5pia^(4))/(128)` |
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