SOLUTION: To 2 decimal places, what is the area enclosed between the curves with equations y=x^2 - ax and y=bx - x^2 when a = 13.8 and b = 5.2?

Algebra ->  Functions -> SOLUTION: To 2 decimal places, what is the area enclosed between the curves with equations y=x^2 - ax and y=bx - x^2 when a = 13.8 and b = 5.2?      Log On


   

Question 1021852: To 2 decimal places, what is the area enclosed between the curves with equations
y=x^2 - ax
and
y=bx - x^2
when a = 13.8 and b = 5.2?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the limits of integration.
y=x%5E2-13.8x
y=5.2x-x%5E2
So,
x%5E2-13.8x=5.2x-x%5E2
2x%5E2-19x=0
x%282x-19%29=0
Two solutions:
x=0
and
2x-19=0
2x=19
x=19%2F2
Integrate.
A=int%28%285.2x-x%5E2-%28x%5E2-13.8x%29%29%2Cdx%2C0%2C19%2F2%29
A=int%2819x-2x%5E2%29%2Cdx%2C0%2C19%2F2%29
A=19%28x%5E2%2F2%29-%282%2F3%29x%5E3%2BC}
A=%2819%2F2%29%2819%2F2%29%5E2-%282%2F3%29%2819%2F2%29%5E3
A%2B%281%2F3%29%2819%2F2%29%5E3
A=6859%2F24
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