Some problems provide the opportunity for more than one mistake.

The Goal

Find the derivative F'(x), where

The Mistakes

Find the mistakes:

1.

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2.

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3.

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4.

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5.

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6.

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7.

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A Correct Solution

(Roll the mouse over the area above to see the corrections in blue)

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.

Visit Calculus Facts > Derivative of an Integral to learn more.