1. ` int_(0)^(1)int_(x)^(x(2-x)) f(x,y)dxdy`

int_(-1)^(1)int_(0)^(2)int_(x-2)^(x+2)(x+y+z)dxdydz

If f(x) =x + int_(0)^(1) (xy^(2)+x^(2)y)(f(y)) dy, "find" f(x) if x and y are independent.

Prove that : int_(0)^(2a) f(x)dx=int_(0)^(a) f(x)dx+int_(0)^(a) f(x)dx+int_(0)^(a) f(2a-x)dx

int_(0)^(a)[f(x)+f(a-x)]dx=

evaluate: int_(0)^(2)int_(3)^(sqrt(y))[1+x+y]*dxdy

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

If int_(0)^(1)f(x)dx=1 and int_(1)^(2)f(y)dy=2 , then int_(0)^(2)f(z)dz=

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If int_(0)^(a//2)f(x)dx=p," then "int_(0)^(a)f(x)dx is equal to