Question

How do you use the trapezoidal rule with n=60 to approximate the area between the curve `y=sinx` from 0 to pi?

Answer 1

See the explanation.

Explanation:

There is no "area between a curve". I assume you want the area beneath the curve (and above the `x` axis).

We use the trapezoidal rule by using the formula.

`T_60 = 1/2 Deltax(f(x_0)+2f(x_1)+2f(x_3)+* * * +2f(x_(n-1)+f(x_n))`

In this case `f(x) = sinx`

`n=60` and `Deltax = (b-a)/n = (pi-0)/60 = pi/60`

`x_0 = 0, x_1=pi/60, x_2 = (2pi)/60, x_3=(3pi)/60, . . . x_(n-1)=((n-1)pi)/60, x_n = pi`

Plug in the numbers and do the arithmetic.
(If permitted, use a computer spreadsheet for all that arithmetic. I got `1.999543`, which is quite close to the exact value of `2`)