Evaluate the following integration: I(f) = integral sign from 0 to 20 of e^(-x) dx

Question

1. Analytically
2. Rectangle method with h= 10,5,4,2,1.
3. Mid-point method with h= 10,5,4,2,1.
4. Trapezoidal method with h= 10,5,4,2,1.
5. Simpson's method with h= 10,5,4,2,1.
6. Using analytical and numerical solutions of 2) to 5) to calculate error e = | I(f) - I(f) | [absolute value of (analytical - numerical)]

Thanks a ton. =)

Answer 1

I will attempt #1.
1.
∫e^-xdx
=-e^-x+C
So for the limits 0 to 20, we get
I=[-e^-x] 0 to 20
=-e^-20-(-e^-0)
=1-e^-20

For the rest, use the appropriate method, and evaluate e^-x at specified intervals to get the required answers.

If you have difficulty with any one of the methods, post your attempt to get further help.