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

1 Answer
Oct 10, 2015

Answer:

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#)