# Numerical integration

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##### Intros

##### Examples

###### Lessons

**Questions Regarding the Midpoint Rule**Approximate $\int^9_4 \sqrt{x} dx$ using Midpoint Rule with 5 sub-intervals.

- Approximate $\int^5_2 \frac{1}{2+x^{2}}$ using Midpoint Rule with 3 sub-intervals.
**Questions Regarding the Trapezoid Rule**Approximate $\int^1_0 e^{x} dx$ using Trapezoid Rule with 4 sub-intervals.

- Approximate $\int^5_1 x^{2} dx$ using Trapezoid Rule with 5 sub-intervals.
**Questions Regarding the Simpsons Rule**Approximate $\int^4_2 \sqrt{x-2} dx$ using Simpsons Rule with 4 sub-intervals.

- Approximate $\int^4_1 \ln (x^{2}) dx$ using Simpsons Rule with 6 sub-intervals.
**Questions Regarding Error Bounds**Let $f(x) = e^{x^{3}}$ consider $\int^1_0 e^{x^{3}} dx$. Assume you know that $|f''(x)| \leq 15e$ and $|f^{(4)}| \leq 585e$ for all $x \in [0, 1]$. If $n$ = 10, then find the following errors: