Question

int(int(6xy^3 x=y..1) y=0..1) dxdy

Answer 1

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

Answer 2

yes it is

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

sure

Answer 8

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

Answer 9

I got 10. Is that what you got?

Answer 10

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

Answer 11

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.

Answer 12

perfect thanks

Answer 13

Everything under the red line.

Answer 14

sorry im comparing right now...

Answer 15

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.

Answer 16

ok i see it

Answer 17

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.

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

no probs.

Answer 24

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

Answer 25

just did it

Answer 26

cheers

Answer 27

so you're getting the same answer?

Answer 28

yes, after remembering the rule it all made sense

Answer 29

good.