Question

In Exercises \(33-36,\) use NINT to evaluate the expression. Find the area enclosed between the \(x\) -axis and the graph of \(y=4-x^{2}\) from \(x=-2\) to \(x=2\)

Short answer

Apply numerical integration on your calculator using the NINT function. The integral to compute is \(\int_{-2}^{2} (4-x^{2}) dx\). The output from the calculator is the desired area.

Step-by-step solution

Understand the Problem

The exercise involves finding the area enclosed by the \(x\) -axis and the curve represented by \(y=4-x^2\) between \(x=-2\) and \(x=2\). Since the problem does not provide a particular method, we'll use numerical integration for this purpose.

Define the Integral

The integral that represents the area enclosed by the curve and the \(x\) -axis from \(x=-2\) to \(x=2\) is the definite integral given by \(\int_{-2}^{2} (4-x^{2}) dx\). This integral will give us the area we are looking for.

Apply Numerical Integration

Use the NINT function on your calculator to compute the numerical integral of the function \(4-x^{2}\) from \(-2\) to \(2\). This will provide the numerical approximation to the area under the curve.

Interpret Results

The result of this numerical approximation is the area enclosed between the given boundaries for the function \(y = 4 - x^{2}\).