Question

How do you approximate of `int sinx(dx)` from `[0,pi]` by the trapezoidal approximation using n=10?

Answer 1

See the explanation section.

Explanation:

To approximate the Integral `int_a^b f(x) dx` using trapezoidal approximation with `n` intervals.

In this question we have:
`f(x) = sinx`
`{a,b] = [0, pi]`, and
`n=10`.

So we get
`Delta x = (b-a)/n = (pi-0)/10 = pi/10`

The endpoints of the subintervals are found by beginning at `a=0` and successively adding `Delta x = pi/10` to find the points until we get to `x_n = b = pi`.

`x_0 = 0`, `x_1 = pi/10`, `x_2 = (2pi)/10`, `x_3 = (3pi)/10` . . . `x_9 = (9pi)/10`, and `x_10 = (10pi)/10 = 10 = b`

Now apply the formula (do the arithmetic) for `f(x) = sinx`.

`T_4=(Deltax)/2 [f(x_0)+2f(x_1)+2f(x_2)+ * * * 2f(x_9)+f(x_10)]`