Question

integrate t^2sqrt(9t^4+4t^2)

does anybody know how i would go about doing this with u substitution?

Answer 1

\[\int\limits_{0}^{1}t^2\sqrt{9t^4+4t^2}dt\]

Answer 2

first off; you can factor the t^2 from the sqrt outside to get t

Answer 3

yh

Answer 4

\[t^3\sqrt{9t^2+4}\]

Answer 5

this you can rewrite as
\[3t ^{3}\sqrt{t ^{2}+(\frac{ 2 }{ 3 })^{2}}\]

Answer 6

now you can think of a trig substitution

Answer 7

trig sub? theres gotta be a way to do this using u-sub. >.<

Answer 8

\[t = \frac{ 2 }{ 3 }\tan \Theta \]

Answer 9

use this substitution; trig identity will come in handy

Answer 10

http://answers.yahoo.com/question/index?qid=20101002183858AAV3Jqm

i think theres an easier way to go about doing this. when i look at this though, i cant keep track of what the person is doing

Answer 11

it will get reduced to
\[\frac{ 32 }{ 81 }\int\limits \tan ^{4}\Theta \sec ^{2}\Theta d \Theta \]

Answer 12

now make the substitution
\[u = \tan \Theta \]

Answer 13

you'll get
\[\frac{ 32 }{ 81 }\int\limits u ^{4} du\]

Answer 14

which you can now easily solve

Answer 15

then plug back u in terms of tan theta

Answer 16

and finally plug back in tan theta in terms of t

Answer 17

and you get the final ans

Answer 18

alrite thanks. are you 100% postive there isnt a way to do this using just u-sub?

Answer 19

oh wait; we are doing definite integral, so whenever you make a substitution the limits on the integral change

Answer 20

in this case it will change twice since we make two substitutions

Answer 21

so in the final step just evaluate the integral to get a number