Chapter 4: Q. 57 (page 373)

Use the Fundamental Theorem of Calculus to find the exact
values of each of the definite integrals in Exercises $19 - 64$ . Use
a graph to check your answer.
$\int_{2}^{4} \frac{3 x}{1 - x^{2}} d x$

Short Answer

Expert verified

The value of expression is $\frac{- 3}{2} \ln (5)$ and the graph is

Step by step solution

Step 1. Given information

An expression is given $\int_{2}^{4} \frac{3 x}{1 - x^{2}} d x$

Step 2. Simplification

Simplify the expression as,

$\int_{2}^{4} \frac{3 x}{1 - x^{2}} d x = 3 \int_{2}^{4} \frac{x}{1 - x^{2}} d x = 3 (\frac{- 1}{2}) {[\ln (x^{2} - 1)]}_{2}^{4} = \frac{- 3}{2} \ln (5) - \frac{3}{2} \ln (3) + \frac{3}{2} \ln (3) = \frac{- 3}{2} \ln (5)$

And the graph is

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Use the Fundamental Theorem of Calculus to find the exact
values of each of the definite integrals in Exercises $19 - 64$ . Use
a graph to check your answer.
$\int_{2}^{4} \frac{3 x}{1 - x^{2}} d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplification

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Use the Fundamental Theorem of Calculus to find the exactvalues of each of the definite integrals in Exercises 19–64. Usea graph to check your answer.∫243x1-x2dx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Discrete Mathematics

Pure Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

Use the Fundamental Theorem of Calculus to find the exact
values of each of the definite integrals in Exercises $19 - 64$ . Use
a graph to check your answer.
$\int_{2}^{4} \frac{3 x}{1 - x^{2}} d x$