[" Evaluate the lollowing "(15-26):],[" 15."int int_(0)^(2)(dx)/(4cos x+2sin x)(]

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)

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (f) int_(0)^(pi)(xdx)/(a^(2)cos^(2)x + b^(2)sin^(2)x)

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

int_(0)^(15)[x^(2)]dx

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

Evaluate : int_0^(π/2) (cos x-sin x)dx .

Evaluate the following intergrals (i) int_(15)^(30) cos (4x - 3)dx (ii) int_0^(30) cos 5 x dx (iii) int_(0)^(30) cos 5 x dx (iv) int_(0)^(10) sec^2 (3x +6)dx

Find the values of the following integrals (i) int_(0)^(2 pi) sin^(2) x cos^(4) x dx