How do you find the antiderivative of #f(x)=-1/2x^3+2x^2-3x-2#?

2 Answers
Jun 2, 2018

#-1/8x^4+2/3x^3-3/2x^2-2x+C#

Explanation:

The antiderivative of the function is basically the integral of the function. So here we have: #int-1/2x^3+2x^2-3x-2 \ dx#.

We use the power rule and the constant rule, which states that,

  • #inta^n \ dx=(a^(n+1))/(n+1)+C#

  • #inta*f(x) \ dx=aintf(x) \ dx#,

respectively.

#=-1/8x^4+2/3x^3-3/2x^2-2x+C#

Jun 2, 2018

#-1/8x^4+2/3x^3-3/2x^2-2x+c#

Explanation:

#"integrate each term using the "color(blue)"power rule"#

#•color(white)(x)int(ax^n)=a/(n+1)x^(n+1)ton!=-1#

#int(-1/2x^3+2x^2-3x-2)dx#

#=-1/8x^4+2/3x^3-3/2x^2-2x+c#

#"where c is the constant of integration"#