Thread: Can someone check this - Area between curves

Find the area between and

I found the integral to be



and after evaluating that i found the area to be 170.66667

Does this seem correct?

Thank you?

Originally Posted by mybrohshi5

Find the area between and

I found the integral to be



and after evaluating that i found the area to be 170.66667

Does this seem correct?

Thank you?

y=x^2-12 is a parabola pointing upwards with vertex at (0,-12) while the other is a parabola pointing downwards with vertex at (0,20). both of them meet at(+-4,4).

Now integrating along the x-axis will lead to complications. better will be to integrate along y-axis.then the integral will be from 20 to -12and the expression will be as in the attachment.

I just tried what you attached and i got 0 for my answer.

Does that seem right?

Thanks for the help

Looking at my original graph again of y=20-x^2 and y=x^2-12 i notice that there is more area above the x axis than below so it doesnt seem right to me that the area is 0. Just from looking at the graph it looks like the area should maybe be a positive number????

Originally Posted by mybrohshi5

Looking at my original graph again of y=20-x^2 and y=x^2-12 i notice that there is more area above the x axis than below so it doesnt seem right to me that the area is 0. Just from looking at the graph it looks like the area should maybe be a positive number????

you are right. the answer comes out to be 0.which is wrong. i am not able to find out my mistake. either there is a mistake in putting the limits(which is less probable) or i put the value of x instead of y to integrate. sorry for the mistake.

Originally Posted by mybrohshi5

Looking at my original graph again of y=20-x^2 and y=x^2-12 i notice that there is more area above the x axis than below so it doesnt seem right to me that the area is 0. Just from looking at the graph it looks like the area should maybe be a positive number????

mistake in putting the limits:

there will be three integrals:

I1=integration(20,4)sqrt(y+12)dy
I2=integration(0,4)sqrt(20-y)dy
I3=integration(0,12)sqrt(20-y)dy

area=I1+I2+I3.

I don't see anything wrong with just doing

as you say in your first post.


which equals 85 and 2/3, not 170 and 2/3.

I believe you made a mistake on your integral. I think it should be




which equals 170 and 2/3

Thank you for the help

Yes, of course!