   Chapter 7.7, Problem 31E

Chapter
Section
Textbook Problem

# (a) Use the Midpoint Rule and the given data to estimate the value of the integral ∫ 1 5 f ( x ) d x . x f(x) 1.0 2.4 1.5 2.9 2.0 3.3 2.5 3.6 3.0 3.8 3.5 4.0 4.0 4.1 4.5 3.9 5.0 3.5 (b) If it is known that − 2 ≤ f ″ ( x ) ≤ 3 for all x, estimate the error involved in the approximation in part (a).

To determine

a) To evaluate: To estimate the value of integral 15f(x)dx by using midpoint rule and the given data.

Explanation

Calculation: From the given table, we have 4 sub-intervals

Here b=5, a=1, n=4    Δ=1

The value of the integral 15f(x)dx=2

To determine

b) To estimate: The error bound

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