How do you evaluate the definite integral #int(x^3-x^2+1)dx# from #[-1,2]#?
1 Answer
Nov 30, 2016
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#
