`int_(0)^( pi/2)[x^(n)+n(n-1)x^(n-2)]dx`

If A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx,B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx for n in N, Then (A)A_(n+1)=A_(n)(B)B_(n+1)=B_(n)(C)A_(n+1)-A_(n)=B_(n+1)(D)B_(n+1)-B_(n)=A_(n+1)

If quad A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx;B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx; for n in N, then

If int_(0)^(pi//2) cos^(n)x sin^(n) x dx=lambda int_(0)^(pi//2) sin^(n)x" dx" , then lambda=

A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx;B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx; for n in N then A_(n+1)=A_(n)( b) B_(n+1)=B_(n)A_(n+1)-A_(n)=B_(n+1)(d)B_(n+1)-B=A_(n+1)

The value of I=int_(0)^(pi//4)(tan^(*n+1)x)dx+(1)/(2)int_(0)^(pi//2)tan^(n-1)((x)/(2))dx is equal to

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

int_(0)^(pi//2)(sin^(n)x)/((sin^(n)x+cos^(n)x))dx=?

For any n in N, int_(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to