Question. A function is defined by:

.

Find and show that .

I cannot get to the final number... I am making a mistake somewhere (or mistakes!) and I'd appreciate your feedback!

First, apply Leibniz Rule for differentiation under integral sign:

Then I deal with the first integral first: differentiate on t, and then integrate on x (using substitution ).

=

Adding the other two components from above, I get the final answer

and substituting , I get , but not the required .