Evaluate each of the following integral: `int_a^b(f(x))/(f(x)+f(a+b-x))dx`

Evaluate of each of the following integral: int_a^b(x^(1//n))/(x^(1//n)+(a+b-x)^(1/n))dx , \ ngeq2

Prove that: int_a^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

If int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=10 , then

The integral int_(0)^(a) (g(x))/(f(x)+f(a-x))dx vanishes, if

Evaluate the following integrals: int_-5^0f(x)dx ,w h e r ef(x)=|x|+|x+2|+|x+5|

The value of the integral int_(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(1 + x) = f(1 - x) (AA x in R) , then the value of the integral I = int_(-7)^(9)(f(x))/(f(x)+f(2-x))dx is

Evaluate the following indefinite integrals. (a) int(dx)/(sqrt(x)) (b) int(dx)/((2x+3)) (c) intsin(2pix+30^(@))dx (d) intsinxcosxdx (e) int(3x^(3)-5x^(2)+2)dx (f) int(2e^(-x//3)dx

Suppose we define the definite integral using the following formula int_a^b f(x)dx=(b-a)/2 (f(x)+f(b)) , for more accurate result for c in (a,b), F(c)=(c-a)/2 (f(a)+f(c))+(b-c)/2(f(b)+f(c)) and when c=(a+b)/2, int_a^b f(x)dx=(b-a)/4(f(a)+f(b)+2f(c))