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.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column