How do you evaluate the definite integral int(x^3-x^2+1)dx from [-1,2]?

1 Answer
Nov 30, 2016

15/4

Explanation:

Use the color(blue)"power rule for integration"

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(intax^ndx=a/(n+1)x^(n+1))color(white)(2/2)|)))

Apply this to each term.

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

=[1/4x^4-1/3x^3+x]_-1^2

=[1/4(2)^4-1/3(2)^3+2]-[1/4(-1)^4-1/3(-1)^3-1]

=(4-8/3+2)-(1/4+1/3-1)

=10/3-(-5/12)=15/4