Question

can anybody explain Integration by parts to me. Or know a good website that explains it well?

Answer 1

My teacher gave us review problems for the final. And one question I completely didn't understand. I was informed that I needed to know integration by parts. But I can't seem to find it in my Calc. book

Answer 2

see http://www.khanacademy.org/math/calculus/integral-calculus/integration_by_parts/v/deriving-integration-by-parts-formula

Answer 3

thanks I'll check this out

Answer 4

thank you that was interesting. but maybe there is another way to solve the problem. Because my teacher solved it in class just not in a way that made any sense to me. It also doesn't seem like he solved it using integration by parts

Answer 5

here is the problem
\[y=\int\limits_{\sqrt{x}}^{x}te ^{t}dt\]

Answer 6

then he made it
\[\int\limits_{\sqrt{x}}^{a}te ^{t}dt+\int\limits_{a}^{x}te ^{t}dt\]

Answer 7

\[-\int\limits_{a}^{\sqrt{x}}te ^{t}dt+\int\limits_{a}^{x}te ^{t}dt\]

Answer 8

\[y \prime=\frac{ \sqrt{x}e ^{\sqrt{x}} }{ 2\sqrt{x} }+xe ^{x}\]

Answer 9

Is that integration by parts?

Answer 10

What did you do in that last step ?

Answer 11

i have no idea lol. I just copied it off the board. Is there something wrong?

Answer 12

I don't see the point he was trying to make. Let me think about it.

Answer 13

ok. At least its not just me. Because I definitely did all the assigned reading and homework and I didn't learn anything close to this

Answer 14

When I asked Hartnn about this yesterday he said Integration by parts is what I needed to use. I didn't go through all these steps though.

Answer 15

ok, the derivation you just posted shows
y' which is the derivative of y (not the integral)

it seems like a demonstration on how to take the derivative wrt x of
\[ \frac{d}{dx} y = \int_{\sqrt{x}}^{x} t\ e^t \ dt \]

you use
http://mathmistakes.info/facts/CalculusFacts/learn/doi/doi.html
to do this, but you have to re-format the problem in the way your professor shows

Answer 16

so it is a different problem than integration by parts... it is how to take the derivative of a definite integral...

Answer 17

ok thanks a ton. Your dedication to helping me is very much appreciated

Answer 18

notice at the bottom of the page I posted are details you need to know to do your problem.
in particular http://mathmistakes.info/facts/CalculusFacts/learn/doi/doil.html
and
http://mathmistakes.info/facts/CalculusFacts/learn/doi/doif.html

Answer 19

ok. I see he was using zeros not a's as the lower part of the integral

Answer 20

ok this makes perfect sense then except I should've made that first part of the answer negative.

Answer 21

yes. I forgot to mention the typo...

Answer 22

Alright well I'm really glad you were able to figure this all out