Michael J. answered • 04/21/15
Tutor
5
(5)
Mastery of Limits, Derivatives, and Integration Techniques
The integral is the same thing as anti-derivative. If the derivative of -cos(x) is sin(x), then go in the reverse direction.
F(x) = ∫sin(x) dx = -cos(x) + C
Next, we evaluate the integral from 0 to t. This means we evaluate
F(t) - F(0)
Substitute the values of 0 and t into the integral.
-cos(t) - (-cos(0)) =
-cos(t) - (-1) =
1 - cos(t)
