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Calculus area
Consider f(x) = x^3 + x^2 + 1 and g(x) = -x^2 + 3x +1
a) Write the integral to compute the area of the region bounded by f and g.
I think you would subtract the bottom function from the top function, but what would the integral of integration be?
Thanks for any help.
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First of all you need to solve for where the two curves intersect.
Solve simultaneously:
f(x) = x^3 + x^2 + 1 and g(x) = -x^2 + 3x +1
x^3 + 2x^2 - 3x = 0
x (x^2 + 2x - 3) = 0
x (x + 3)(x - 1) = 0
so the two curves actually intersect at 3 spots... at
x = -3, y = -17
x = 0, y = 1
and x = 1, y = 3
Between -3 and 0, we see that f(x) > g(x) and between 0 and 1, we see that g(x) > f(x)
Therefore, the the area bounded by the two curves should be given by the formula:
integral from -3 to 0 of [f(x) - g(x)] + integral from 0 to 1 of [g(x) - f(x)]
:-)
Hope that helps... and sorry about the notation... the math tags don't seem to be working...