Question

Let f be an odd function, that is f(-x) =-f(x). We know that integral from 0^5 f(x) = 3. Then using properties of definite integrals we conclude that...

Answer 1

the second equation is like this\[\int\limits_{0}^{5}fx=3\]

Answer 2

is it pretty simple? just the zero replaces with -5 and -3 instead of 3?

Answer 3

There's a bunch of assumptions you can make really. But if it is an odd function, then:
\[\int\limits_{-a}^{a}f(x)dx = 0\] So.....I suppose you could conclude:
\[\int\limits_{-5}^{0}f(x)dx = -3\]

Answer 4

ok but thankfully this a actually a multiple choice question so all my options have 5 on the top and -5 on the bottom of the integral sign

Answer 5

Ah. Yeah, if a function is odd then it's as I said:
\[\int\limits_{-a}^{a}f(x)dx = 0\]
Might as well throw it out there, but if a function is even then:
\[\int\limits_{-a}^{a}f(x)dx = 2\int\limits_{0}^{a}f(x)dx\]