Question

solve \[\int\limits_{}^{} \sqrt{a^{2}-x^{2}} \] using integration by parts

Answer 1

\[\int\limits_{}^{} \sqrt{a^{2}-x^{2}} dx\]

Answer 2

it's specific that you use integration by parts?

Answer 3

or is that just your preference?

Answer 4

yep.. i knw it can b done easily using a substitution. but gotta do it by parts.. :(

Answer 5

well you have no choice...you use \[ u = \sqrt{a^2 - x^2}\]
\[dv = dx\]

Answer 6

\[du = -\frac{x}{\sqrt{a^2 - x^2}}\]

\[v = x\]

Answer 7

does that help?

Answer 8

\[uv - \int vdu\]
\[\implies x\sqrt{a^2 - x^2} + \int \frac{x^2}{\sqrt{a^2-x^2}}dx\]
now that is integrable easily right?

Answer 9

do i still need to proceed? or do you know what to do now?

Answer 10

wait i'l try n tel ya

Answer 11

sure. go for it

Answer 12

i stand corrected by my earier words...\(\int \frac{x^2}{\sqrt{a^2 - x^2}}dx\) is NOT an easy integral =))

Answer 13

you're gonna have to use trig sub one way or another...

Answer 14

This is a fairly evil integral (look up the answer in a table), and as you say, integration by parts is not going to get you anywhere. I'm not sure I can work it out myself without reference to Strang or some other source. Do you know Strang's book? It's online.

Answer 15

http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/

Answer 16

Or Paul's notes must have it too.

Answer 17

actuallly that last integral i presented \[\int \frac{x^2}{\sqrt{a^2-x^2}}dx\]
is solveable...but it involves integration by parts + trig sub

Answer 18

so it's still possible to use IPB

Answer 19

Maybe so, looking at the answer, but it'll be several steps.

Answer 20

@lgbasallote
yep.. i too agree with u.

Answer 21

but anyway...yes it is evil

Answer 22

http://integral-table.com/integral-table.html#SECTION00007000000000000000
#29

Answer 23

not that evil :)
try \(x=asin\theta\)

Answer 24

then simplify; not that hard i suppose

Answer 25

@Mimi_x3
using a substitution i okay.. but my bro said his teacher asked him 2 do it usin IBP.. thats da prob

Answer 26

didnt igba use IBP then reduced it to that integral? that is what i can see above; from that trig sub and you're done

Answer 27

im talking about this integral \[\int\limits\frac{x^{2}}{\sqrt{a^{2}-x^{2}}} dx\]

Answer 28

yep.. I think theres noway to solve \int \frac{x^2}{\sqrt{a^2 - x^2}}dx without using trig sub? isnt it?

Answer 29

\[\int\limits \frac{x^2}{\sqrt{a^2 - x^2}}dx\]

Answer 30

well if you want to do integration by parts twice; i think it is possible i havent tried tho. but why bother? since you already did integration by parts once? just trig sub for the last step

Answer 31

itz nt me whois bothering.. itz ma brother.. :D thnk all of ya for da help.