Question

Integral help:

Answer 1

\[\int\limits x^3+x^4\tan(x)dx\]

Answer 2

can u guys give me advice about what to pick for u when doing substitution or if I would need to set it up before doing so

Answer 3

first use linearity of integrals:
\[\int f(x)+g(x)~dx=\int f(x)dx+\int g(x)dx\]

Answer 4

I have limits on this problem, could I do this without the limits and then apply the limits of integration after that?

Answer 5

so you have \[\int x^3dx+\int x^4\tan xdx\]

Answer 6

This doesn't look too easy to be honest, without limits it makes it harder, definitely tell us as much info as possible about the problem @kl0723

Answer 7

ok my limits are from -pi/4 to pi/4

Answer 8

hmm the second part i think you need integration by part as a start

Answer 9

with those limits the problem is trivial

Answer 10

according to the book I should be able to apply substitution without the use of "by parts" method, but I don't really know how to set up the problem

Answer 11

review the integration of odd functions from -a to a

Answer 12

oh i see

Answer 13

i didn't pay attention to odd even thingy hehe

Answer 14

4 times by parts? it's very annoying... teachers!!! ha

Answer 15

just check your textbook you should be able to see it :)

Answer 16

@SolomonZelman there is not by part

Answer 17

I thought I saw that somewhere in the thread.

Answer 18

if \(f(x)\) is an odd function defined on [-a,a] then

\[\int\limits_{-a}^{a}f(x)dx=0\]

Answer 19

oh wow :P

Answer 20

yes 0 is the solution :)

Answer 21

@xapproachesinfinity @Kainui and @Zarkon Thank you! I'll make sure to review this

Answer 22

welcome :)
i didn't do anything though
the credit is to @Zarkon and @Kainui lol

Answer 23

what if I had an even function?

Answer 24

if \(f(x)\) is even then

\[\int\limits_{-a}^{a}f(x)dx=2\int\limits_{0}^{a}f(x)dx\]

Answer 25

it would be 2int(f(x))dx from [0,a]

Answer 26

you would still need to do work

Answer 27

odd are the best ;)

Answer 28

hehe sure they are lol
i don't want go integrate by part all that stuff hehe

Answer 29

in what I wrote above we are obviously assuming the \(f\) is integrable.

Answer 30

just to be complete

Answer 31

Here's a picture, just a random odd function and even function. You can see how the area under the curve for an odd function will exactly cancel left and right, while an even function you have double on left and right, so you can just double half the integral, it's not something you should spend time memorizing.