Question

Use the trapezoidal rule to approximate the area under the semicircle.

Answer 1

The trapezoidal rule involves dividing the semicircle into trapezoids and calculating their areas to approximate the total area under the curve.

Step-by-step explanation:

The trapezoidal rule can be used to approximate the area under the semicircle. The idea is to divide the semicircle into small trapezoids, and then calculate the sum of the areas of these trapezoids to approximate the total area under the curve. Here's how:

1. Divide the interval of the semicircle into small subintervals.
2. For each subinterval, calculate the height of the trapezoid by evaluating the function corresponding to the semicircle at the endpoints.
3. Calculate the area of each trapezoid using the formula A = ((b-a)/2)(h1 + h2), where 'a' and 'b' are the endpoints of the subinterval and 'h1' and 'h2' are the heights of the trapezoid.
4. Add up the areas of all the trapezoids to get the approximate area under the semicircle.