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Calculus/Definite Integrals

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Expert: - 4/26/2011


Question
Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.

f(x)= 3x-6  [-1, 3]

f(x) = 2x - x^2 [0,2]

Kind of lost here. Any clarification would be greatly appreciated!

Answer
If f(x) = 3x - 6, the integral, known as F(x) = 3(x^2)/2 - 6x
and the answer would be F(3) - F(-1).
F(3) = 27/2 - 18 = 27/2 - 36/2 = - 9/2.
F(-1) = 3/2 + 6 = 15/2.
All that is left is to find F(3) - F(-1)

If f(x) = 2x - x^2, then F(x) = x^2 - x^3/3
and the answer would be F(2) - F(0); not the F(0) is 0, so the answer is just F(2).
That is, 2^2 - 2^3/3 = 4 - 8/3 = 12/3 - 8/3 = 4/3.

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