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" 18.Fित कifre "int(0)^(a)(dx)/(x+sqrt(a...

" 18.Fित कifre "int_(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

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Prove that : int_(0)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

int_(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx=(pi-2)/(4)

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The value of the expression (int_(0)^(a)x^(4)sqrt(a^(2)-x^(2))dx)/(int_(0)^(a)x^(2)sqrt(a^(2)-x^(2))dx)=

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int_(0)^((pi)/(4))sqrt(1+sin2x)dx

int_(0)^(pi) sqrt((1+cos 2x)/(2))dx=

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int_(0)^((pi)/(4)) sqrt(1+sin 2x) dx =