The Fundamental Theorem of Calculus Exercises

Answer

Answer

 for t > 0

Answer

Answer

Answer

Define

Then

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First flip the limits of integration and the sign so we have the constant as the lower limit of integration:

If we define

then

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In order to take this derivative we first have to split the integral up.

Now we use the chain rule on each piece. If

then

Putting the pieces together,