[" Iuustration "25.5" Find the mistake in the following "],[" evaluation of the integral "I=int_(0)^( pi)(dx)/(1+2sin^(2)x)]

Find the mistake of the following evaluation of the integral I=int_(0)^( pi)(dx)/(1+2sin^(2)x)I=int_(0)^( pi)(dx)/(cos^(2)x+3sin^(2)x)=int_(0)^( pi)(sec^(2)xdx)/(1+3tan^(2)x)=(1)/(sqrt(3))[tan^(-1)(sqrt(3)tan x)]_(0)^( pi)=0

Evaluate the integral int_(0)^(pi) x sin^(3)x dx

Evaluate the integrals int_(0)^((pi)/(2))(sin x)/(1+cos^(2)x)dx

Evaluate the integral I=int_(0)^(pi//4) (sinx+cosx)/(9+16sin2x) dx

Find the mistake in the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) , then : I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]_pi^0=0

Find the mistake in the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) , then : I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]_pi^0=0

Evaluate the integrals : I = int_(-pi)^(pi) sin^(2) (x/2) dx ,

Find the mistake of the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]pi0=0

Evaluate the following integral: int_(0)^( pi/2)(dx)/(4cos x+2sin x)

Evaluate the following integrals : int_(0)^(pi/2)(dx)/(4sin^(2)x+5cos^(2)x)