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 3 cos(4x) x dx, n = 8 1 (a) the Trapezoidal Rule 1 (b) the Midpoint Rule 2 (c) Simpson's Rule

The correct question is contained in the first attached file.

a) The trapezoidal rule answer

0.433490

b) The midpoint rule answer

1.186075

c) The Simpson's rule answer

1.106143

Step-by-step explanation:

These numerical methods are means of estimating definite integrals by finding the area under the curve of the function between two points.

a) The solution for the trapezoidal rule method is presented in the 2nd attached image to this solution.

b) The solution for the midpoint rule method is presented in the 3rd attached image to this solution.

c) The solution for the Simpson's rule method is presented in the 4th attached image to this solution.

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5

c

step-by-step explanation: