1. ## Integration...having neither x-values

given that ∫15x^2 dx = 3430, and x=a and x=-a. Find the value of the constant a.

I'm not quite sure how to approach solving for a.
I(x) = 5x^3

So would I set that equal to 3430?
5x^3=5430
x^3=686
x= approx. 8.8?

7^3 is 343 ...

3430/10 = 343 .. but how could I get to that (justify it anyways)

Thanks so much, I really want to understand how to do this, I'm just confused on where to go from here.

Thanks!

2. Originally Posted by rubbersoul923
given that ∫15x^2 dx = 3430, and x=a and x=-a. Find the value of the constant a.

I'm not quite sure how to approach solving for a.
I(x) = 5x^3

So would I set that equal to 3430?
5x^3=5430
x^3=686
x= approx. 8.8?

7^3 is 343 ...

3430/10 = 343 .. but how could I get to that (justify it anyways)

Thanks so much, I really want to understand how to do this, I'm just confused on where to go from here.

Thanks!
$\displaystyle \int_{-a}^{a}15x^2dx=3430 \iff 5x^{3}\bigg|_{-a}^{a}=3430 \iff 5(a^3-(-a)^3)=3430$

This gives

$\displaystyle 10a^3=3430 \iff a^3=343$

just solve from here.

3. Using symmetry solve for $\displaystyle a$ where $\displaystyle \int_0^a 15x^2~dx = \frac{3430}{2}$