Evaluate:
`int_(0)^(pi//2)sinxdx`

Explanation

To evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \sin x \, dx \), we will follow these steps:

### Step 1: Identify the Integral
We need to evaluate the definite integral of the function \( \sin x \) from \( 0 \) to \( \frac{\pi}{2} \).

### Step 2: Find the Antiderivative
The first step in evaluating the integral is to find the antiderivative of \( \sin x \). The antiderivative of \( \sin x \) is:
\[ -\cos x \]

### Step 3: Apply the Limits of Integration
Now, we will apply the limits of integration from \( 0 \) to \( \frac{\pi}{2} \):
\[ \int_{0}^{\frac{\pi}{2}} \sin x \, dx = \left[-\cos x\right]_{0}^{\frac{\pi}{2}} \]

### Step 4: Evaluate at the Upper Limit
Now, we will evaluate the antiderivative at the upper limit \( \frac{\pi}{2} \):
\[ -\cos\left(\frac{\pi}{2}\right) = -0 = 0 \]

### Step 5: Evaluate at the Lower Limit
Next, we will evaluate the antiderivative at the lower limit \( 0 \):
\[ -\cos(0) = -1 \]

### Step 6: Subtract the Two Results
Now, we subtract the value at the lower limit from the value at the upper limit:
\[ 0 - (-1) = 0 + 1 = 1 \]

### Final Result
Thus, the value of the integral is:
\[ \int_{0}^{\frac{\pi}{2}} \sin x \, dx = 1 \]

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