Question

fhdt

Answer 1

i dont know how to solve WITHOUT by parts

Answer 2

this doesn't look smooth even with parts
http://www.wolframalpha.com/input/?i=%5Cint+%28x%5E3%2Bx%5E4tan%28x%29%29+dx

Answer 3

wow that big :P

Answer 4

are you really sure this is not a definite integral ?

Answer 5

oh my goooooooooooood

Answer 6

its an odd one :)

Answer 7

then just check it is odd or not

Answer 8

the function is odd if f(x) = -f(-x)

Answer 9

what book is this?

Answer 10

\[\int\limits_{-a}^{a}f(x)dx=0\]
for odd functions thats a property

Answer 11

f(x) is given calculate f(-x_ then check if f(x)=-f(-x)
if satisfied then odd

Answer 12

and if
f(x)=f(-x) then even

Answer 13

\[f(x)=x^3+x^4\tan(x)\\f(-x)=(-x)^3+(-x)^4.\tan(-x)=-x^3-x^4\tan(x)\\=-(x^3+x^4\tan(x))=-f(x)\\so\\f(x)=-f(-x)\]

Answer 14

thats why it odd get it?

Answer 15

yes
and there is also a property for even ,it is
\[\int\limits_{-a}^{a}f(x)dx=2. \int\limits_{0}^{a}f(x).dx\]
if f(x)=even
but u dont have to worry about it, here f(x) is odd so it will be 0

Answer 16

familiar with area interpretation of definite integral ?

Answer 17

I see you're thinking of integral as antiderivative

Answer 18

There is another interpreation -
Definite integral gives you the "signed area" under curve

Answer 19

an odd function is symmetric about the point (0, 0)

Answer 20

think of sin(x) or any other familiar odd function

Answer 21

the area below x axis(-) and above x axis(+) kill each other for odd functions. see :
http://prntscr.com/59dfan

Answer 22

thats okay, we are still talking about odd function property itself

Answer 23

np :) i think it is best to try to understand definite integrals using area because most definite integrals you deal with in calc1 require symmetry