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" 10."int(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)...

" 10."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)

Prove that (pi)/(6)

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

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)=

int_(0)^(2)x^(2)sqrt(4-x^(2))dx=

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

int (10^(pi/2)dx)/(sqrt(10^(-x)-10^(x)) ) =

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

int_(0)^(10) (5-sqrt(10x-x^(2))) dx=

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