   Chapter 13, Problem 35RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate ∫ 1 3 2 x 3 d x (a) exactly.(b) using the Trapezoidal Rule with n = 4 (to 3 decimal places).(c) using Simpson's Rule with n = 4 (to 3 decimal places).

(a)

To determine

To calculate: The exact value of the integral 132x3dx.

Explanation

Given Information:

The provided integral is 132x3dx.

Formula used:

According to power rule of integrals,

xndx=xn+1n+1+C

Calculation:

Consider the integral, 132x3dx

Rewrite the integral as,

132x3dx=213x3dx

(b)

To determine

To calculate: The value of the integral 132x3dx to 3 decimal places. Use the Trapezoidal rule with n=4 divisions.

(c)

To determine

To calculate: The value of the integral 132x3dx to 3 decimal places. Use Simpson's Rule with n=4.

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