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

Oct 10, 2015

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 $f \left(x\right) = \sin x$

$n = 60$ and $\Delta x = \frac{b - a}{n} = \frac{\pi - 0}{60} = \frac{\pi}{60}$

${x}_{0} = 0 , {x}_{1} = \frac{\pi}{60} , {x}_{2} = \frac{2 \pi}{60} , {x}_{3} = \frac{3 \pi}{60} , . . . {x}_{n - 1} = \frac{\left(n - 1\right) \pi}{60} , {x}_{n} = \pi$

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 $2$)