Question

What is the value of integral 0 to 4 3x^2 sqrt (x^3 + 1) dx?

Answer 1

well, what do you think you can do?

Answer 2

That's sort of why I'm on here...to get a little help.

Answer 3

Hint\[
\int_0^4 3x^2\sqrt{x^3+1}~dx = \int_0^4\sqrt{x^2+1}~d(x^3+1)
\]

Answer 4

well u=x^3+1

Answer 5

u = x^3+1, so your du is going to be equal to dx times the derivative of u.

Answer 6

so, what happens if you do a substitution?

Answer 7

like the one solomon suggested

Answer 8

Ok so du = dx(3x^2), right?

Answer 9

yes
du=3x^2 dx

Answer 10

yep, so now, can you integrate your remaining function?