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

Answer 1

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

Answer 2

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

Answer 3

I finally get it. Thanks!