why is integral cos(x) dx from x=0 to pi/2 positive 1 and not negative? This is what i've got:
D(cos(x)) = -sin(x).
-sin(pi/2) - (-sin(0)) = -1 - (-0) = -1

Question

why is integral cos(x) dx from x=0 to pi/2 positive 1 and not negative? This is what i've got:
D(cos(x)) = -sin(x).
-sin(pi/2) - (-sin(0)) = -1 - (-0) = -1

anonymous · Answer

The derivative of what function gives you cos(x)?
It's sin(x).
Ddx sin(x) = cos(x). Not negative! Careful!

anonymous · Answer

You are dealing with the integral which is the antiderivative of the function evaluated from (0,pi/2)$$\int\limits_{0}^{\pi/2} \cos(x)dx = \sin(\pi/2) - \sin(0) = 1 - 0 = 1$$

anonymous · Answer

I finally get it. Thanks!