Evaluate the definite integral from 0 to π/2 of sin(x) dx.

To evaluate the definite integral of sin(x) from 0 to π/2, we start by determining the antiderivative of sin(x). The integral of sin(x) is -cos(x). Therefore, we can express the definite integral as follows:

[

\int_0^{\frac{\pi}{2}} \sin(x) , dx = \left[-\cos(x)\right]_0^{\frac{\pi}{2}}

]

Next, we evaluate this at the bounds. First, we substitute π/2:

[

-\cos\left(\frac{\pi}{2}\right) = -0 = 0

]

Then we substitute 0:

[

-\cos(0) = -1

]

Putting this together, we calculate the result:

[

\int_0^{\frac{\pi}{2}} \sin(x) , dx = 0 - (-1) = 1

]

Thus, the value of the definite integral from 0 to π/2 of sin(x) is 1. This solidifies that the chosen answer is correct as it aligns with the computed value of the integral.