### Home > APCALC > Chapter 6 > Lesson 6.5.1 > Problem6-179

6-179.

Using the Fundamental Theorem of Calculus, what is $\frac { d } { d x }$$\int _ { 3 x } ^ { x ^ { 2 } } e ^ { t ^ { 2 } } d t$?

This expression is NOT equal to $e^{(x^4)} − e^{(3x)^2}$.
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 substituted $x^{2}$ and $3x$ into the antiderivative, creating composite functions...
so when you got to step 2, you would have to use the Chain Rule.

$2xe^{(x^4)} − 3e^{(3x)^2}$
Notice that the Chain Rule was applied to each bound.