Step 1:

Using our knowledge of common integrals, we can find the integral as follows:

[latex]\large{\int_{0}^{\frac{\pi}{2}}(\sin(x)) dx = -\cos(x)|_{0}^{\frac{\pi}{2}}}[/latex]

Step 2:

Now, we can apply the fundamental theorem of calculus. This states that:

[latex]\large{\int_{a}^{b}f(x) dx = F(b) – F(a)}[/latex]

Thus, we have:

[latex]\large{\int_{0}^{\frac{\pi}{2}}(\sin(x)) dx }[/latex]

[latex]\large{= [-\cos(\frac{\pi}{2})] – [ -\cos(0)] }[/latex]

[latex]\large{ =  0\:-\: (-1) = 1}[/latex]

Step 3:

So, our final answer is:

[latex]\large{\int_{0}^{\frac{\pi}{2}}(\sin(x))dx = 1}[/latex]

Solution Complete!