Asked by caitlyn
Find the area of the indicated region. Enclosed by y = −x and y = x4
Answers
Answered by
Reiny
intersection:
x^4 = -x
x^4 + x = 0
x(x^3 +1) = 0
x(x+1)(x^2 -x + 1)= 0
2 real solutions,
x = 0 or x = -1
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2C+y+%3D+-x
area = ∫(-x - x^4) from -1 to 0
= [- x^2/2 - x^5/5] form -1 to 0
= (0 - (-1 -(-1)/5)
= 1 - 1/5
= 4/5
x^4 = -x
x^4 + x = 0
x(x^3 +1) = 0
x(x+1)(x^2 -x + 1)= 0
2 real solutions,
x = 0 or x = -1
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2C+y+%3D+-x
area = ∫(-x - x^4) from -1 to 0
= [- x^2/2 - x^5/5] form -1 to 0
= (0 - (-1 -(-1)/5)
= 1 - 1/5
= 4/5
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.