SOLUTION: Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx. (Your answer must include the antiderivative.) Use a graph of the

Algebra ->  Finance -> SOLUTION: Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx. (Your answer must include the antiderivative.) Use a graph of the      Log On


   

Question 1029355: Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.
(Your answer must include the antiderivative.)
Use a graph of the function to explain the geometric meaning of the value of the integral.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
int%28%28x%5E3-6x%29%2Cdx%29=x%5E4%2F4-3x%5E2%2BC
Evaluated,
int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=%283%5E4-0%5E4%29%2F4-3%283%5E2-0%5E2%29
int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-27
int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=81%2F4-108%2F4
int%28%28x%5E3-6x%29%2Cdx%2C0%2C3%29=-27%2F4
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The integral is equal to the area of the curve, below the x-axis is negative, above the x-axis is positive.
Since more area is below the x-axis, the total area is negative.