Find the simplest antiderivative of the function. Pay attention to which variable is being used.
f(x) = 10x9
F(x) = x10
f(x) = x3
F(x) = ln |x| (we need the absolute value signs in this case to make sure F is defined everywhere that f is defined).
f(t) = -sin t
F(t) = cos t
f(x) = -cos x
F(x) = -sin x
f(t) = sec2 t
F(t) = tan t
f(x) = e2x
f(x) = 5x ln 5
F(x) = 5x
F(x) = -x-1 or
f(x) = x2 + 3x – 5
Evaluate the integral.
There are two ways to do this problem. The way that probably comes to mind first is to use the FTC:
The other way is to notice that x3 is an odd function. When we integrate any odd function from -a to a, we get 0. So when we integrate x3 from -1 to 1, we get 0.
Either 1 – e-1 or should be an acceptable answer. We like the one with the fraction better than the one with the negative exponent.
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