Some problems provide the opportunity for more than one mistake.

The Goal

Find

The Mistakes

Find the mistakes:

1.

(Roll the mouse over the math to see a hint in red)

2.

(Roll the mouse over the math to see a hint in red)

A Correct Solution

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

Explanations

In the first mistake the antiderivative is computed incorrectly - the negative sign is needed.

In the second mistake a common sign error is made. If F(x) is an antiderivative of the integrand (the function in the integral), the value of the definite integral from a to b is F(b)-F(a), which applies even if F(x) has a minus sign in front of it. So if F(x) = -e^-x, then F(b)-F(a) = (-e^-b) - (-e^-a) = e^-a - e^-b.