×
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 62e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 62e

×

# Solved: Fractional powers Use the indicated substitution

ISBN: 9780321570567 2

## Solution for problem 62E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendentals | 1st Edition

4 5 1 310 Reviews
27
5
Problem 62E

Problem 62E

Fractional powers

Use the indicated substitution to convert the given integral to an integral of a rational function. Evaluate the resulting integral.

Step-by-Step Solution:

Problem 62E

Fractional powers Use the indicated substitution to convert the given integral to an integral of a rational function. Evaluate the resulting integral.

Step 1

Definition of a Rational Function;  A rational  function is a function that is a fraction  and has a property that  both its  numerator  and denominator  are polynomials . In other words , R(x) is  a rational function if R(x) =  where p(x) and q(x) are both polynomials , and q(x) recall that a polynomial is any function of the form  f(x) = a +bx+ c+.............. +n, where a,b , c ……………….n  are all real numbers and the exponents of each x is a non -negative integer.

Proper fraction definition ; In a rational fraction  , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

The sum of two proper fractions is a proper fraction.

Example;

Partial fractions Depending upon the nature of factors of Denominator ;

1. When the denominator has non-repeated linear factors;

A non - repeated linear factor (x-a) of denominator corresponds a partial fraction of the form  , where A is a constant to be determined’

If g(x) = (x-a)(x-b)(x-c)............(x-n), then we assume that

=  ++ +...............+

Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a,b ,c ….n.

Step 2 of 2

##### ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Fractional powers Use the indicated substitution to convert the given integral to an integral of a rational function. Evaluate the resulting integral.” is broken down into a number of easy to follow steps, and 22 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 62E from 7.4 chapter was answered, more than 253 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 62E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: integral, convert, Fractional, function, given. This expansive textbook survival guide covers 112 chapters, and 5248 solutions.

#### Related chapters

Unlock Textbook Solution