## leonasmart 3 years ago check below for question:using integration by substitution

1. leonasmart

|dw:1335086576446:dw|

2. TomLikesPhysics

I would set u=x^3. so du=3x^2dx so x^2dx=1/3 * du. So you can rewrite it as 1/3 * (u-5)^0.5du and integrate that more easily. Of course you might wanna pull the 1/3 out and just integrate (u-5)^0.5 du and than just put it back in the end when you resubstitute.

3. leonasmart

do the working out for me to c plzz

4. bmp

Remember what I said to you. Look outside the square root, you have x^2. There must be a c such that: cx^2 = du/dx for u = x^3 - 5. That would imply that 3x^2 = cx^2 -> c = 3, so multiply by 3/3.

5. TomLikesPhysics

I end up with: 2/9 * (x^3-5)^(3/2) + C

6. bmp

$\frac{3}{3} \int\limits_{a}^{b}x^2\sqrt{x^3 - 5}dx = \frac{1}{3} \int\limits_{u}^{v}\sqrt{u}du = \frac{1}{3} \int\limits_{u}^{v}u^{\frac{1}{2}}du$

7. leonasmart

wait u is x^3-5 rite? and u is 3x^2?

8. bmp

Yeah, du = 3x^2. That's what I said, I belive.

9. bmp

du = 3x^2dx to be more precise.

10. bmp

@TomLikesPhysics That is correct :-)

11. leonasmart

12. leonasmart

what did i do wrong??

13. bmp

Remember that you have to divide by n+1, so you divide by 3/2. That's the same as multiplying by 2/3, so you have (1/3)(2/3) = 2/9. The rest is ok, well done :-)

14. Chlorophyll

You're absolutely correct!