4. `int_0^2(2x+1)dx`

int_0^4 (2x-1) dx

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

int_0^2 |1-x|dx

Show that int_(0)^(2)(2x+1)dx = int_(0)^(5)(2x+1)+int_(5)^(2)(2x+1)

int_0^1(2-3x+x^2)dx

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

Find int_0^2 (x^2+1)dx as the limit of a sum.

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

int_0^1f(x)dx=1,\ int_0^1xf(x)dx=a ,\ int_0^1x^2f(x)dx=a^2,\ t h e n\ int_0^1(a-x)^2f(x)dx equals a. 4a^2 b. 0 c. 2a^2 d. none of these

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 .