- #1
Mhorton91
- 42
- 1
Homework Statement
Use areas to evaluate the integral f(x)=5x+√(25-x2) on the following intervals
a) [-5,0]
b) [-5,5]
Homework Equations
∫f(x) + g(x) = ∫f(x) + ∫g(x)
also Area of a circle = pi(r)2
The Attempt at a Solution
[/B]
My first several attempts have centered around evaluating the integral on the first interval, from -5 to 0.
I have attempted to break it into---
∫5x + ∫√(25-x2.
After graphing y=5x, I get a point at (-5, -25) which I use to construct a triangle of base (-)5, and height (-)25.
Using the 1/2(base)(height) formula I get 125/2 square units.
The graph of the latter y=√(25-x2 appears to be the upper hemisphere of a circle of radius 5, centered around the origin.
Limiting it to the interval [-5,0] Leaves me with 1/4 of a circle radius 5, or
1/4(pi)(radius2)
To which I end up getting 25pi/4
so then I attempt to combine them with the rule of sums listed above.. My class uses an online homework system, and the answer I am entering is
(25pi/4)+125/2
That answer doesn't appear to be correct.
I had to take a year off after Calc 1, and this is my first assignment in Calc 2.. I'm trying to get back on the learning curve.Also, here is a screen shot of the actual problem in case my write up was confusing.
I appreciate any push in the proper direction!
Marshall