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

Evaluate the following integral: int_0^(pi//2)1/(a^2sin^2x+b^2cos^2x)dx

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

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 the integral int_0^oox/((1+x)(1+x^2))dx is (pi^)/2 (b) (pi^)/4 (c) (pi^)/6 (d) pi/3

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

The value of [tan{pi/4+1/2sin^(-1)(a/b)}]^(-1)

The value of the definite integral (1)/(pi)int_((pi)/(2))^((5 pi)/(2))(e^(tan^(-1)(sin x)))/(e^(tan^(-1)(sin x)+e^(tan^(-1)(cos x)))dx is )

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

The value of the integral int_(-(3 pi)/(4))^((pi)/(4))((sin x+cos x)/(e^(x-(pi)/(4))+1))dx(A)0(B)1(C)2(D) none of these