Evaluate : (i) `int_(0)^(1) sin^(-1)((2x)/(1+x^(2)))dx` , (ii) `int_(0)^(1) (xtan^(-1)x)/((1+x^(2))^(3//2))dx` (iii) `int_(a)^(b) sqrt((x-a)(b-x))dx,
Evaluate :
(i) `int_(0)^(1) sin^(-1)((2x)/(1+x^(2)))dx` , (ii) `int_(0)^(1) (xtan^(-1)x)/((1+x^(2))^(3//2))dx`
(iii) `int_(a)^(b) sqrt((x-a)(b-x))dx, a gt b`
(iv) `int_(0)^(sqrt(3)) tan^(-1)((2x)/(1-x^(2)))`
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Correct Answer - (i) `pi/2 - ln 2` , (iii) `(4-pi)/(4sqrt(2))` , (iii) `- (pi)/(8)(b-a)^(2)` , (iv) `pi (1-(1)/(sqrt(3))) - ln 5`
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