Find the area bounded by y=8-x^2 and y=x^2.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We first determine the points where the curves y = 8 - x^2 and y = x^2, meet.

8 - x^2 = x^2

=> x^2 = 4

=> x = 2 , x = -2

Now we find the integral of 8 - x^2 - x^2 between the limits x...

See
This Answer Now

Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your Subscription

We first determine the points where the curves y = 8 - x^2 and y = x^2, meet.

8 - x^2 = x^2

=> x^2 = 4

=> x = 2 , x = -2

Now we find the integral of 8 - x^2 - x^2 between the limits x = -2 and x = 2

Int [ 8 - 2x^2 ]

=> 8x - 2x^3/3

Between the limits x = -2 and x = 2

8x - 2x^3/3 - 8x + 2x^3/3

=> 8*2 - 2*8/3 + 8*2 - 2*8/3

=> 32 - 32/3

=> 64/3

The area bounded by the curves is 64/3.

Approved by eNotes Editorial Team