Question

Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and left endpoints. (Round your answers to four decimal places.)

Answer 1

x = 0 to x = pi/2 divided into 4 equal parts. (pi/2 - 0) / 4 = pi/8.
x = 0, pi/8, pi/4, 3pi/8, pi/2 are the points.

Answer 2

The width of each rectangle is pi/8.
Find the height of each rectangle by using the LEFT endpoint as specified in the problem.
For example, the height of the first rectangle is f(0) (where x = 0 is the left endpoint).
The height of the second rectangle is f(pi/8) (where x = pi/8 is the left endpoint).
Find the area of each of the four rectangles and add them up.

Answer 3

so would it be pi/8(f(pi/2)+f(3pi/8)+f(pi/4)+f(pi/8))?

Answer 4

\[
\frac{\pi}{8}*\left \{ f(0)+f(\pi/8) + f(\pi / 4) + f(3\pi/8)\right \}
\]

Answer 5

Yes! Okay that is great! Thank you so much!

Answer 6

You are welcome.