Question

Integrate using symmetry

Answer 1

check if f(-x)=-f(x) if it does then the integral from -a to a is zero else if f(-x)=f(x) the integral from -a to a equals two times the integral from 0 to a if its neither of these evaluate the integral normally. Google odd and even functions for more info.

Answer 2

hmm.. f(-x)=f(x) is it? so its odd? then how do i evaluate the integral? its abit unclear

Answer 3

when f(x) is an odd function,
\(\huge \int \limits_{-b}^bf(x)dx = 0\)

Answer 4

so do i still need to integrate the equation? and equate to 0? i dont get it ):

Answer 5

no you need not integrate anything!

Answer 6

since the function was odd and was integrated from -something to + something
the total area under that curve (the odd function) will be 0
so, its integration will turn out to be = 0

Answer 7

in that case, the answer is 0 then?

Answer 8

absolutely :)

Answer 9

how about if it is even?

Answer 10

if f(x) is even
\(\huge \int \limits_{-b}^bf(x)dx =2\huge \int \limits_{0}^bf(x)dx \)

Answer 11

because the area from -b to 0 and 0 to be will be same!

Answer 12

***0 to 'b'

Answer 13

then you would actually need to integrate the function

Answer 14

i see, integrate from 0 to b then, neglecting the -b, then multiplying the answer by 2?

Answer 15

yes.

Answer 16

understood, thank you!(:

Answer 17

welcome ^_^