Common Calculus Mistakes
Definite Integral 
Some problems provide the opportunity for more than one mistake. The Goal
Find The Mistakes
Find the mistakes:
(Roll the mouse over the math to see a hint in red) (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}. 
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