Question

Integration prove question: http://puu.sh/1ZYIB

Answer 1

You want to use the fundamental theorem of Calculus here.

Answer 2

looks like the trick is to use a u-substitution for a-x

Answer 3

For the left hand integral:
\[\int\limits_{0}^{a}f(x)dx = F(a)-F(0)\]
For the right hand integral:
\[\int\limits_{0}^{a}f(a-x)dx\]
Let \[u = g(x) = a-x\]
Then,
\[du = -dx\]
\[g(0)=a \enspace \text{and}\enspace g(a) = 0\]
Thus, our integral becomes,
\[-\int\limits_{g(0)}^{g(a)}f(u)du=-\int\limits_{a}^{0}f(u)du=-[F(0)-F(a)]=F(a)-F(0)\]
which is the same as the left hand integral and we are done.

Answer 4

@jtvatsim hey i dont understand why did you put g(a) an g(0) top and bottom limits?