### Home > CALC > Chapter 6 > Lesson 6.3.2 > Problem6-96

6-96.

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

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

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.

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