CPM Homework Help : CALC Problem 6-96

Using the Fundamental Theorem of Calculus, find: $\frac { d } { d x } \int _ { 3 x } ^ { x ^ { 2 } } e ^ { t ^ { 2 } } d t$ .

Hint 1:

This expression is NOT equal to $e^{(x4)} − e^{(3x)2}$ .
Explain why not.

Hint 2:

If you did not know about the Fundamental Theorem of Calculus,
you would probably evaluate this expression by doing the following steps:
Step 1: Integrate.
Step 2: Differentiate.
As a result of step 1, you would have plugged $x^{2}$ and $3x$ into the antiderivative, creating composite functions...
so when you got to step 2, you would have to use the Chain Rule.

Answer:

$2xe^{(x4)} − 3e^{(3x)2}$ .
Notice that the Chain Rule was applied to each bound.