The hint is a really good one.
Even function
Odd function
Fundamental theorem of calculus
When you integrate an even function then you obtain an odd function.
When you integrate an odd function then you obtain an even function.
I'm confused about this question so some help would be appreciated.
"Suppose f is an even function and g is an odd function. Explain for any a>0, Integral (from -a to a) f =2 Integral (from 0 to a) f and Integral (from -a to a) g=0.
First make a sketch of such functions and look at net areas. Can you also explain these results with the Fundamental Theorem of Calculus?
(hint: if a function is even (or odd) then its derivative is odd (or even); and if a function is
odd then any anti-derivative is even and if a function is even then the anti-derivative that passes through the origin is odd (but not the other anti-derivatives!)).
I have no clue how to proceed with this question. I tried graphing even and odd functions. I graphed y=x^2 as well as y=x^4 and I noticed that the graphs had the same magnitude of area from the origin to a and -a, respectively. Odd functions, I used y=x^3 and x^5 and these graphs had the same area from -a to 0 and 0 to a but opposite sides of the x-axis. However, I can't seem to piece together what this means so any help would really help me out.