Question

Evaluate ∫(0,2) ∫(y^2,4) (sqrt(x))sinxdxdy...by using integration by parts

Answer 1

normally is fine too, without integration by parts. But integration by parts would be more helpful!

Answer 2

...HMM well that's an odd notation... is it:
\[\int^2_0\int^4_{y^2}\sin(x)\sqrt{x}\phantom{.}dx\phantom{.}dy\]

Answer 3

yes!

Answer 4

ALRIGHT!

Well I would first find the primitive of \(\sin(x)\sqrt{x}\) first before doing anything!

Just to point out, the integral is not very nice according to this:
http://www.wolframalpha.com/input/?i=integral+of+sin%28x%29sqrt%28x%29

BUT I'LL DO MY BEST!

Answer 5

Ok, by the way. If you are doing it the normal way it is much nicer switching the order. But if not it will be very difficult. But I will get extra credit if I use parts and I really need the extra credit haha.

Answer 6

Haha I give up...I tried but I think im not getting anywhere... here is what I had so far... but I don't think that's going anywhere...SORRY.

\[\eqalign{
&\int\sin(x)\sqrt{x}\phantom{.}dx \\
=&\int \sin(x)u\phantom{.}dx\to\phantom{space}u=\sqrt{x}\to u^2=x\to dx=2u\phantom{.}du\\
=&\int\sin(u^2)(u)(2u)du\\
=&2\int u^2\sin(u^2)du \\
=&2\int a\phantom{.}db \\
&\\
a&=u^2\phantom{...}db=\sin(u^2) \\
da&=2u\phantom{....}b=\small{\int}\sin(u^2) \\
&\\
=&2\int a\phantom{.}db \\
=&2\left[ab-\int b\phantom{.}da\right] \\
=&2\left[u^2\int\sin(u^2)-\int2u\left(\int\sin(u^2)\right)\right] \\
}\]

Answer 7

its ok thanx though!!

Answer 8

Could you help me do the integral with by switching the order?

Answer 9

@zpupster hey, where are you in the problem