Questions: Find the area of the region bounded by the function and the x-axis on the interval [0, π/2]. y = sin(x)

Solution Steps

To find the area of the region bounded by the function \( y = \sin(x) \) and the \( x \)-axis on the interval \([0, \frac{\pi}{2}]\), we need to compute the definite integral of the function over the given interval. The integral of \( \sin(x) \) from 0 to \(\frac{\pi}{2}\) will give us the desired area.

To find the area of the region bounded by the function \( y = \sin(x) \) and the \( x \)-axis on the interval \( \left[0, \frac{\pi}{2}\right] \), we need to compute the definite integral:

\[ A = \int_{0}^{\frac{\pi}{2}} \sin(x) \, dx \]

The integral of \( \sin(x) \) can be evaluated as follows:

\[ A = -\cos(x) \bigg|_{0}^{\frac{\pi}{2}} = -\cos\left(\frac{\pi}{2}\right) - \left(-\cos(0)\right) = 0 - (-1) = 1 \]

The area of the region bounded by the function \( y = \sin(x) \) and the \( x \)-axis on the interval \( \left[0, \frac{\pi}{2}\right] \) is approximately \( 0.9999999999999999 \), which can be rounded to \( 1 \).

Final Answer