# Thread: approximate the integral Simpson's Rule & trapezoidal rule

1. ## approximate the integral Simpson's Rule & trapezoidal rule

As always your help is greatly appriciated!

Approximate the integral $\int_{0}^{1}x^4dx ; n =6$, by

a.) first applying Simpson's Rule and
b.) then applying the trapezoidal rule

2. Originally Posted by Yogi_Bear_79
As always your help is greatly appriciated!

Approximate the integral $\int_{0}^{1}x^4dx ; n =6$, by

a.) first applying Simpson's Rule and
The arithmetic I am not going to do.
Since $n$ is even so you can apply Simpons rule.
$\int_0^1 x^4 dx\approx$ $\frac{1}{3}\big( (0)^4+4(1/6)^4+2(2/6)^4+$ $4(3/6)^4+2(4/6)^4+4(5/6)^4+(6/6)^4 \big) \frac{1}{6}$

3. Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?

4. Originally Posted by Yogi_Bear_79
Thanks for your help. Can anyone help with the trapezoidal rule section of the problem?
Same idea.
$\frac{1}{2}\big( 0^4+2(1/6)^4+2(2/6)^4+2(3/6)^4$ $+2(4/6)^4+2(5/6)^4+(6/6)^4 \big)\cdot \frac{1}{6}$