Q. 58 Use the Fundamental Theorem of C... [FREE SOLUTION]

Chapter 4: Q. 58 (page 373)

Use the Fundamental Theorem of Calculus to find the exact
values of each of the definite integrals in Exercises $19 鈥� 64$ . Use
a graph to check your answer.
${鈭�}_{0}^{1} \frac{2^{x} - 3^{x}}{4^{x}} d x$

Short Answer

Expert verified

The value of integral is $(\frac{1}{2} (\frac{1}{\ln (\frac{1}{2})}) - \frac{1}{\ln (\frac{1}{2})}) - (\frac{3}{4} (\frac{1}{\ln (\frac{3}{4})}) - \frac{1}{\ln (\frac{3}{4})})$

And the graph is

Step by step solution

Step 1. Given information

An expression is given as ${鈭�}_{0}^{1} \frac{2^{x} - 3^{x}}{4^{x}} d x$

Step 2. Evaluating integral

Simplify the integral as,

${鈭�}_{0}^{1} \frac{2^{x} - 3^{x}}{4^{x}} d x = {鈭�}_{0}^{1} {(\frac{2}{4})}^{x} d x - {鈭�}_{0}^{1} {(\frac{3}{4})}^{x} d x = {鈭�}_{0}^{1} {(\frac{1}{2})}^{x} d x - {鈭�}_{0}^{1} {(\frac{3}{4})}^{x} d x = {[\frac{1}{\ln (\frac{1}{2})} {(\frac{1}{2})}^{x}]}_{0}^{1} - {[\frac{1}{\ln (\frac{3}{4})} {(\frac{3}{4})}^{x}]}_{0}^{1} = (\frac{1}{2} (\frac{1}{\ln (\frac{1}{2})}) - \frac{1}{\ln (\frac{1}{2})}) - (\frac{3}{4} (\frac{1}{\ln (\frac{3}{4})}) - \frac{1}{\ln (\frac{3}{4})})$

And the graph is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the Fundamental Theorem of Calculus to find the exact
values of each of the definite integrals in Exercises $19 鈥� 64$ . Use
a graph to check your answer.
${鈭�}_{0}^{1} \frac{2^{x} - 3^{x}}{4^{x}} d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Logic and Functions

Mechanics Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Use the Fundamental Theorem of Calculus to find the exactvalues of each of the definite integrals in Exercises 19鈥�64. Usea graph to check your answer.鈭�012x-3x4xdx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Logic and Functions

Mechanics Maths

Statistics

Discrete Mathematics

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 $19 鈥� 64$ . Use
a graph to check your answer.
${鈭�}_{0}^{1} \frac{2^{x} - 3^{x}}{4^{x}} d x$