Some problems provide the opportunity for more than one mistake.

The Goal

Find the derivative F'(x), where

The Mistakes

Find the mistakes:

1.

Need a hint? Look carefully at the red part:

2.

Need a hint? Look carefully at the red part:

3.

Need a hint? Look carefully at the red part:

4.

Need a hint? Look carefully at the red part:

5.

Need a hint? Look carefully at the red part:

6.

Need a hint? Look carefully at the red part:

7.

Need a hint? Look carefully at the red part:

A Correct Solution

Explanations

By what is often called the Second Fundamental Theorem of Calculus,

so all that needs to be done is to write down the integrand (the function inside the integral) with the variable t replaced by x. All of the attempted solutions are pure fiction, although the only error in Mistake 4 is that it uses the incorrect variable.