If I_n = int_0^(pi/2) (sin^2 nx)/(sin^2 x) dx , then
Evaluation of definite integrals by subsitiution and properties of its : I_(1)=int_(a)^(pi-a)xf(sinx)dx,I_(2)=int_(a)^(pi-a)f(sinx)dx then I_(2)=……..
Prove that I_(1),I_(2),I_(3)"..." form an AP, if (i) I_(n)=int_(0)^(pi)(sin2nx)/(sinx)dx (ii) I_(n)=int_(0)^(pi)((sinnx)/(sinx))^(2)dx .
Fundamental theorem of definite integral : I=int_(0)^(1)(sinx)/(sqrtx)dx and J=int_(0)^(1)(cosx)/(sqrtx)dx then which of the following statement is true ?
Evaluate int_(0)^(pi/2)logsinxdx
Evaluate int_(0)^(pi)(xsinx)/(1+cos^(2)x)dx
Prove that int_(0)^(pi/2)sin2xlogtanxdx=0 .
If I_(n)=int_(0)^(pi)(1-sin2nx)/(1-cos2x)dx then I_(1),I_(2),I_(3),"….." are in
Method of integration by parts : I_(1)=int sin^(-1)x dx and I_(2)= int sin^(-1) sqrt(1-x^(2))dx then.....