Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
$\int_{2}^{4} \frac{1}{4 - 3 x} d x$

Ans: The exact value of, $\int_{2}^{4} \frac{1}{4 - 3 x} d x = - \frac{1}{3} (\ln 8) + \frac{1}{3} (\ln 2)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

given,

$\int_{2}^{4} \frac{1}{4 - 3 x} d x$

Step 2. The objective is to determine the exact value of the definite integral.

The exact value is calculated as shown below,

$\begin{aligned} \int_{2}^{4} \frac{1}{4 - 3 x} d x \\ = - \frac{1}{3} [\ln (| 4 - 3 x |)]_{2}^{4} \\ = - \frac{1}{3} [\ln (| 4 - 3 (4) |) - \ln (| 4 - 3 (2) |)] \\ = - \frac{1}{3} [\ln (8) - \ln (2)] \\ = - \frac{1}{3} (\ln 8) + \frac{1}{3} (\ln 2) \end{aligned}$

Therefore, the exact value is localid="1648629053226" $- \frac{1}{3} (\ln 8) + \frac{1}{3} (\ln 2)$

Step 3. Check

The required graph is,

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Calculus

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Short Answer

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
$\int_{2}^{4} \frac{1}{4 - 3 x} d x$

Step by Step Solution

Step 1. Given information.

Step 2. The objective is to determine the exact value of the definite integral.

Step 3. Check

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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
$\int_{2}^{4} \frac{1}{4 - 3 x} d x$