_N3WTON_
- 350
- 3
Homework Statement
Use an iterated integral to find the area of the region bounded by the graphs of:
f(x) = sin(x)
g(x) = cos(x)
between:
x = \frac{\pi}{4} and x = \frac{5\pi}{4}
Find two solutions, one using a vertical representative rectangle and another using a horizontal representative rectangle.
Homework Equations
Definite Integral Equation
The Attempt at a Solution
I had no issue finding the solution using the vertical representative rectangle, here is my solution:
A = \int_{\frac{\pi}{4}}^{\frac{5\pi}{4}} \int_{cos(x)}^{sin(x)} dy dx
A = \int_{\frac{\pi}{4}}^{\frac{5\pi}{4}} (sin(x) - cos(x)) dx
A = 2\sqrt{2}
The problem I am having is trying to solve this problem using a horizontal representative rectangle. I understand that the solution will be the same, but I can't even seem to set up the problem properly. Would I have to define the two fractions:
\frac{\pi}{4} and \frac{5\pi}{4}
as functions of y and then make the trigonometric functions constant and then integrate?
Last edited: