Question

Use the trapezoidal rule, the midpoint rule, and Simpson's rule

to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 5 1 7 cos(3x) x dx, n =
4

Answer 1

To approximate the given integral, we can use the Trapezoidal rule, Midpoint rule, and Simpson's rule.

Step-by-step explanation:

To approximate the given integral using numerical integration methods, we can use the Trapezoidal rule, Midpoint rule, and Simpson's rule.

For the Trapezoidal rule, we divide the interval into n subintervals, calculate the function values at the endpoints and midpoints of each subinterval, and then sum up the areas of the trapezoids formed.

For the Midpoint rule, we divide the interval into n subintervals, calculate the function values at the midpoint of each subinterval, and then sum up the areas of the rectangles formed.

For Simpson's rule, we divide the interval into n subintervals (n must be even), calculate the function values at the endpoints, midpoints, and the midpoint of each subinterval, and then sum up the areas of the parabolic segments formed.