Question

(1) Find the exact value of ∫sin x dx between 0 & 2
(2) Use the midpoint approximation (n = 10) to approximate the integral.
(3) Use the trapezoidal approximation (n = 20) to approximate the integral.
(4) Use Simpson's rule approximation (n = 20) to approximate the integral.

Answer 1

An integral can be defined as follows:
\[\Large\lim_{n\rightarrow \infty}\sum_{i=1}^nf(x_I^*)\Delta x\]Where \(\Delta x = \frac{b-a}{n}\), which the size of each interval. While \(x_i^*\) is just some point on that interval, and different approximations will pick different points in the interval. For example the midpoint will pick the \(x_i^*\) in the middle.

Answer 2

You should look in your text book about the approximations.

Answer 3

ok.