Solving an integral at a certain value.

[intervade]

Ok, as an example if I have the integral from 1 to a of (3x^2+2x)dx = 5 , how would I go about doing this?

If I integrate this I get x^3+x^2 = 5, now where do I limits of integration come in to play? How do I solve for a? Or is this even the correct way to go about doing this?

 

[wjm11]

integral from 1 to a of (3x^2+2x)dx = 5 , how would I go about doing this?

If I integrate this I get x^3+x^2 = 5, now where do I limits of integration come in to play? How do I solve for a?

You are off to a good start. Plug your limits of integration into your x^3+x^2 expression, and set that result equal to 5. Just solve for "a" then.

 

[BigGlenntheHeavy]

\(\displaystyle \int_{1}^{a}(3x^{2}+2x)dx \ = \ 5\)

\(\displaystyle \implies \ a^{3}+a^{2}-7 \ = \ 0, \ a \ = \ 1.6311\)