Evaluate the integral from [-2,0] of (x^2+x)dx

Question

parthkohli · Answer

First the indefinite integration.$$\int x^2 + x~ dx   = \dfrac{x^3}{3} + \dfrac{x^2}{2}+C$$Let's just say that the integral is $g(x)$. So you have to find $g(upper~limit) - g(lower~limit)$

anonymous · Answer

how did you get the x^3/3 and the x^2/2?

parthkohli · Answer

The Power Rule?$$\int x^n dx = \dfrac{x^{n+1}}{n+1}$$

anonymous · Answer

Okay. So if the final answer for this is supposed to be 2/3, how do you get that by subtracting the lower limit from the upper limit?

parthkohli · Answer

Subtracting the INTEGRALS at the upper and lower limit, that is$$\left(\dfrac{0^3}{3} + \dfrac{0^2}{2}\right) - \left(\dfrac{(-2)^3}{3} + \dfrac{(-2)^2}{2}\right)$$

anonymous · Answer

That makes so much sense now..  Thank you!!

parthkohli · Answer

You're welcome!