**Question: ** Find a simplified expression (involving a sum and a limit) for the area under the curve \(f\left( x \right)=x{{e}^{x}}\) between *x* = 0 and *x* = 2. You should simplify to the point where you no longer have any *x*’s in your expression but you do not need to evaluate the sum or limit.

## Calculus: Calculus, General Integration – #28819

**Question: **Integrate the following functions:

(a) \(f\left( x \right)=2{{x}^{3}}-3{{x}^{2}}+1\) between 0 and 1

(b) \(f\left( x \right)=6{{x}^{2}}+18x\) between -3 and 0

**Question: **Integrate the following functions:

(a) \(f\left( x \right)=2{{x}^{3}}-3{{x}^{2}}+1\) between 0 and 1

(b) \(f\left( x \right)=6{{x}^{2}}+18x\) between -3 and 0