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• 27 cos(x) dx 37 2

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 21CR

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Concept explainers

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

a. Use the Trapezoidal Rule to approximate the integral. (Round to four decimal places.)

b. Estimate the error in using the approximation. Express the answer rounded to three decimal places.

c. Determine the number n of subintervals needed to guarantee that an approximation is correct to within 0.0001

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

To Determine :-

(a) The trapezoidal rule to approximate the integral.

$\int_{\frac{3 π}{2}}^{2 π} \frac{\cos (x)}{x} d x$

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