Question

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

Answer 1

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 \(g(upper~limit) - g(lower~limit)\)

Answer 2

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

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

You're welcome!