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Applying a suitable change of the variable, find the followingdefiniteintegrals : (a)int_(0)^(2) (dx)/((sqrtx - 1) + sqrt((x + 1)^(3))) (b)int_(0)^(a) (dx)/(x + sqrt(a^(2) - x^(2))) (c)int_(1)^(2) (dx)/(x (1 + x^(4)))(d)int_(sqrt((3a^(2)+ b^(2) )//2))^(sqrt((a^(2) + b^(2))//2)) (xdx)/(sqrt((x^(2) -a^(2))(b^(2) - x^(2)))) |
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Answer» (b) `(pi)/(4) ` (c)`(1)/(4) In "" (32)/(17)` (substitution`X^(4) = t`) (d)`(pi)/(4) ` (substitution`x^(2) = a^(2) cos^(2) t + b^(2) SIN^(2) t`) |
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