`int_0^2 |1-x|dx`

int_0^2||x-1|-x|dx

Evaluate the integral I=int_(0)^(2)|x-1|dx .

Evaluate the following definite integral: int_0^2 1/(4+x-x^2)dx

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

int_0^(2a)f(x)dx is equal to a. 2int_0^af(x)dx b. 0 c. int_0^af(x)dx+int_0^af(2a-x)dx d. int_0^af(x)dx+int_0^(2a)f(2a-x)dx

If int_0^1e^-x^2dx=a , then find the value of int_0^1x^2e^-x^2dx in terms of a .

Evaluate: int_0^1|5x-3|dx (ii) int_0^pi|cosx|dx (iii) int_(-5)^5|x-2|dx (iv) int_(-1)^1e^(|x|)dx (v) int_0^2|x^2+2x-3|dx (v) int_1^4(|x-1|+|x-2|+|x-3|)dx (vi) int_(-1)^2|x^3-x|dx

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

int_(0)^(1)x^2dx

Evaluate the following integrals as limit of sums: int_0^2(x+4)dx (ii) int_0^2(2x+1)dx