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Integrals with general bases Evaluate the following

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 19E Chapter 6.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 19E

Problem 19E

Integrals with general bases Evaluate the following integrals.

Step-by-Step Solution:
Step 1 of 3

Solution 19E Step_1 x Exponential function; Exponential functions have the form f(x) = a . Where ‘a’ is the base , and x is the exponent (or power) . If ‘a’ is greater than ‘1’ the function continuously increases in value as x increases. A special property of exponential functions is that the slope of the function also continuously increases as x increases. x Example ; the graph of y = 2 is ; NOTICE: As x increases , y also increases As x increases , the slope of the graph also increases. The curve passes through (0, 1). All exponential curves of the form f(x) = a , passes through (0,1) , if a>0. The curve doesn’t passes through the x -axis .It just gets closer and closer to the x -axis as we take smaller and smaller x values. Let a is exponential function , and it is continuous for all x.So , the integral of x a is ; a dx = a ( x 1 ln(a) Step-3 Now , we have to evaluate Now , from the above step -2 , the integral value of 1 x (10) dx = ((10) ( 1 = ( 99 ) 1 . 10 ln(10) 1 Therefore , (10) dx = ( 99 ) 1 . 10 ln(10) 1

Step 2 of 3

Chapter 6.7, Problem 19E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Integrals with general bases Evaluate the following