The value of the integral `int_0^(pi/4) dx/(a^2cos^2x+b^2sin^2x)=` (A) `1/(ab)tan^-1(b/a)(a,bgt0)` (B) `1/(ab)tan^-1(b/a)(a,blt0)` (C) `pi/4(a=1,b=1)` (D) none of these

int_(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(1)/(ab)tan^(-1).(b)/(a)(a,bge0)

Prove that int_0^(pi/2)(dx)/(a^2cos^2x+b^2sin^2x)=pi/(2ab),a,b>0

Evaluate: int_(0)^(pi/4)(dx)/(a^(2)sin^(2)x+b^(2)cos^(2)x)=(1)/(ab)tan^(-1)(a/b) , where a,b>0

Evaluate: int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x))dx (a) piab (b) pi^(2)ab (c) (pi)/(ab) (d) (pi)/(2ab)

If int(dx)/(cos2x+3sin^(2)x)=(1)/(a)tan^(-1)(b tanx)+c, then ab=

The value of int_0^(pi/2) (dx)/(1+tan^3 x) is (a) 0 (b) 1 (c) pi/2 (d) pi

The values of the definite integral int_0^((3pi)/4)((1+x)sinx+(1-x)cosx)dx , is (A) 2tan((3pi)/8) (B) 2tan(pi/4) (C) 2tan (pi/8) (D) 0

The value of int_(0)^((pi)/(2))(dx)/(1+tan^(3)x) is (a) 0(b)1(c)(pi)/(2)(d)pi

If [x] denotes the integral part of x and a=int_(-1)^0 (sin^2x)/([x/pi]+1/2)dx, b=int_0^1 (sin^2x)/([x/pi]+1/2)d (x-[x]) , then (A) a=b (B) a=-b (C) a=2b (D) none of these