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 .