# Math Help - Area of Region

1. ## Area of Region

Sketch the region enclosed by and . Decide whether to integrate with respect to or . Then find the area of the region.

I am not looking for the answer, just the name of the topic. I have no idea where to start and was hoping I could use the book to find out how to approach this problem. Thanks. The hw is due in an hour, and i still have 2 more problems to go!

2. OK so i started by setting them equal to each other. then I solved for x.

I got (+,- 5/9,6.25) then I subtracted y upper from y lower.

I am trying to do the problem, but I just cant get it.

Can anyone help?

Thanks.

3. I think im on the right track, I just seem to be missing a fundamental step.

4. Here is the graph. it is easier to integrate with respect to x. to find the limits of the integration, solve 4x^2 = 5x. obviously one limit will be zero, find the other one. then integrate 5x - 4x^2 since 5x is the higher function

i'm off to bed, you're on your own

5. Originally Posted by xcelxp
OK so i started by setting them equal to each other. then I solved for x.

I got (+,- 5/9,6.25) then I subtracted y upper from y lower.

I am trying to do the problem, but I just cant get it.

Can anyone help?

Thanks.
for the limits of integration:

5x = 4x^2
=> 4x^2 - 5x = 0
=> x(4x - 5) = 0
=> x = 0 or 4x - 5 = 0
so x = 0 and x = 5/4

so the limits of integration are 0 up to 5/4

the area is given by:

int{0:5/4}(5x - 4x^2)dx
--
if there is anything you're unsure about, ask now, i'll be in bed in about a minute, i'm already falling asleep while sitting here

what is the other question by the way?

6. Just wanted to let you know that your explanation really helped

Ans: ((5/2)(5/4)^2-(4/3)(5/4)^3) - ((5/2)(0)^2-(4/3)(0)^3)

Ty so much, I gave you your thanks!

7. Originally Posted by xcelxp
Just wanted to let you know that your explanation really helped

Ans: ((5/2)(5/4)^2-(4/3)(5/4)^3) - ((5/2)(0)^2-(4/3)(0)^3)

Ty so much, I gave you your thanks!
that seems like the right answer? is it? what about the other question? what explanation, are you talking about the post where i mentioned the fundamental theorem of calculus? you should be sure to look that up by the way, it's VERY important

8. by the way I figured it out before you wrote that explanation with the numbers, now Im working on:

Sketch the region enclosed by , , and . Decide whether to integrate with respect to or . Then find the area of the region.

9. Yup I understand the fundamental theorem now but there is one othe rproblem that is giving me a problem, but the hw is due before 3 am and its 2:55 I doubt ill get everything in on time