Question 972760: I need to find the area between y = −x^2−x+30 and the x-axis
Thank you
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! y = −x^2 −x +30
find the two zeros of this function
−x^2 −x +30 = 0
multiply both sides of equation by -1
x^2 +x -30 = 0
(x+6)*(x-5) = 0
x = -6 and 5
now integrate the formula and evaluate the result for x = 5 and -6
let Z stand for integration, then
Z −x^2 −x +30 = -x^3/3 -x^2/2 +30x
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evaluate for x = 5
-5^3/3 -5^2/2 +30*5 = -125/3 -25/2 +150 = 95.833333333
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evaluate for x = -6
-6^3/3 -6^2/2 +30*(-6) = -(-216)/3 -36/2 -180 = −126
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Area = 95.833333333 - (-126) = 221.833333333 approx 221.83
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