Question

Graph the integrand and use geometry to evaluate the integral. ∫^8,(lower #)-8 (8 - IxI)dx

Answer 1

I can't understand the way you wrote the boundaries.
Is this what it's supposed to look like?\[\Large\bf\sf \int\limits_{-8}^8 8-|x|\;dx\]

Answer 2

yes that is exactly it

Answer 3

So graphing the function \(\Large\bf\sf y=8-|x| \) gives us something like this.

Answer 4

And from here, we don't need the integral anymore.
We can use basic geometry to solve it.

We're looking for the `area under the curve`.
Or in other words, `the area of this triangular region`.

We can break it up into a couple of right triangles if you don't remember how to find the area of an isosceles triangle.

Answer 5

so area is 1/2bh?

Answer 6

For a right triangle? Yah sounds good!

Answer 7

i dont think i understand how to get the answer :( so you take the area of the two triangles and add them up?
because the answer to the problem is 41/4

Answer 8

Hmm that answer is not correct.
The answer should be 64.

Are you sure you pasted the question correctly? D:

Answer 9

Or maybe just looked at the answer to a different question by mistake? <:o

Answer 10

you were right! i was looking at the wrong question! THANK YOU SO MUCH!!!

Answer 11

oh cool :)