Asked by Fred
Find the area enclosed between the curves y=(x-1)^2 and y=5-x^2.
Answer is 9. Thanks for any help provided
Answer is 9. Thanks for any help provided
Answers
Answered by
Reiny
First you need their intersection:
(x-1)^2 = 5-x^2
x^2 - 2x + 1 = 5 - x^2
2x^2 - 2x - 4 = 0
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2 or x = -1
area = ∫ (5-x^2 - (x^2 - 2x + 1) )dx from -1 to 2
= ∫ (-2x^2 + 2x + 4)dx from -1 to 2
= easy from here
picture of your problem:
https://www.wolframalpha.com/input/?i=plot+y%3D(x-1)%5E2+and+y%3D5-x%5E2
(x-1)^2 = 5-x^2
x^2 - 2x + 1 = 5 - x^2
2x^2 - 2x - 4 = 0
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2 or x = -1
area = ∫ (5-x^2 - (x^2 - 2x + 1) )dx from -1 to 2
= ∫ (-2x^2 + 2x + 4)dx from -1 to 2
= easy from here
picture of your problem:
https://www.wolframalpha.com/input/?i=plot+y%3D(x-1)%5E2+and+y%3D5-x%5E2
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