SOLUTION: How to find the integral of y=0.1x^2 between the domain? We have to create a flower petal as part of our assignment so it will form a design in a quilt. So i am assuming that wi

Algebra ->  Functions -> SOLUTION: How to find the integral of y=0.1x^2 between the domain? We have to create a flower petal as part of our assignment so it will form a design in a quilt. So i am assuming that wi      Log On


   

Question 964045: How to find the integral of y=0.1x^2 between the domain?
We have to create a flower petal as part of our assignment so it will form a design in a quilt. So i am assuming that with the two functions you would have to integrate the functions to find the area so then it can be found out what the area of shaded to unshaded ratio is.
The two functions that form this petal are:
y=0.1x^2
y= sqrt (10x)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the limits of integration.
sqrt%2810x%29=0.1x%5E2
10x=0.01x%5E4
10x-0.01x%5E4=0
x%2810-0.01x%5E3%29=0
Two solutions:
x=0
and
10-0.01x%5E3=0
0.01x%5E3=10
x%5E3=1000
x=10
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So then,
A=int%28%28sqrt%2810x%29-0.1x%5E2%29%2Cdx%2Cx=0%2C10%29
A=sqrt%2810%29%282%2F3%29x%5E%283%2F2%29-x%5E3%2F30%2BC
Then evaluating between the limits,
A=%282%2F3%29100-100%2F3
A=100%2F3