## anonymous 5 years ago int(int(6xy^3 x=y..1) y=0..1) dxdy

1. anonymous

Is your problem$\int\limits_{0}^{1}\int\limits_{y}^{1}6xy^3dxdy$?

2. anonymous

yes it is

3. anonymous

Okay, just give me a sec to do something non-mathematical. I can help you.

4. anonymous

ok, cool. i got 1/4, can you tell me if that's right? when ever you're done though

5. anonymous

Okay...I scratched it out and got 1/4 too. You know what you're doing.

6. anonymous

yeah but i'm have a problem with another one...is it ok to ask you one more?

7. anonymous

sure

8. anonymous

ok it's another double...int(int(5sin(x+y) x=0..pi/2) y=0..pi/2) dxdy

9. anonymous

I got 10. Is that what you got?

10. anonymous

i keep getting stuck...this is the third time trying to do it again

11. anonymous

It might be easier for me to scan what I did and attach then write it out...have a look through if and ask questions.

12. anonymous

perfect thanks

13. anonymous

Everything under the red line.

14. anonymous

sorry im comparing right now...

15. anonymous

That's okay. I'll be online for a while. Just post when you're ready. If I don't respond 'immediately', I'm away from the computer.

16. anonymous

ok i see it

17. anonymous

I think you're getting trapped by not just accepting that the other variable is just a constant when you integrate over the other in a double integral.

18. anonymous

your fourth step is different from mine. i dont understand how you went from cos (pi/2 + y) to it becoming sin y

19. anonymous

We get very used to thinking of x and y as things that vary, rather than stand still.

20. anonymous

You can use the double angle formula. You'll see I did that expansion in the top right corner (under the red line).

21. anonymous

$\cos(\frac{\pi}{2}+y)=\cos \frac{\pi}{2}\cos y - \sin \frac{\pi}{2}\sin y$$=0 \times \cos y + (- 1) \times \sin y=-\sin y$

22. anonymous

thank you so much. i would have never remembered that rule

23. anonymous

no probs.

24. anonymous

when you're done and you're satisfied, it'd be great if you could click the 'become a fan' link :)

25. anonymous

just did it

26. anonymous

cheers

27. anonymous

so you're getting the same answer?

28. anonymous

yes, after remembering the rule it all made sense

29. anonymous

good.