Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the value of n. Round the answers to four decimal places and compare the results with the exact value definite integral. ∫9 4 √xdx, n=8.

Answer and Step-by-step explanation: The Trapezoidal and Simpson's Rules are method to approximate a definite integral.

Trapezoidal Rule evaluates the area under the curve (definition of integral) by dividing the total area into trapezoids.

The formula to calculate is given by:

The definite integral will be:

Simpson's Rule divides the area under the curve into an even interval number of subintervals, each with equal width.

The formula to calculate is:

The definite integral will be:

Calculating the definite integral by using the Fundamental Theorem of Calculus:

Comparing results, note that Simpson's Rule is closer to the exact value, i.e., gives better approximation to the exactly value calculated by the fundamental theorem.

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3