   Chapter 6, Problem 12TYS ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Use Simpson’s Rule with n   = 4 to approximate ∫ 0 1 9 x e 3 x d x .Compare your result with the exact value of the definite integral.

To determine

To calculate: The approximate value of 019xe3xdx using the Simpson’s Rule with n=4 and compare the result with the exact value of the definite integral.

Explanation

Given Information:

The definite integral is 019xe3xdx,n=4.

Formula used:

Simpson’s Rule:

If a function f is continuous on [a,b], then

abf(x)dx=(ba3n)[f(x0)+4f(x1)+2f(x2)+4f(x3)++4f(xn1)+f(xn)]

Calculation:

Calculation to get exact value:

Consider the definite integral 019xe3xdx.

019xe3xdx=[9x(e3x3)]019(e3x3)dx=[3xe3x]013e3xdx=3e3[e3x]01=3e3(e31)

Simplify as:

019xe3xdx=2e3+141

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