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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9.4 - Problem 36e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9.4 - Problem 36e

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# Approximating definite integrals Use a Taylor | Ch 9.4 - 36E

ISBN: 9780321570567 2

## Solution for problem 36E Chapter 9.4

Calculus: Early Transcendentals | 1st Edition

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Problem 36E

Problem 36E

Approximating definite integrals Use a Taylor series to approximate the following definite integrals. Retain as many terms as needed to ensure the error is less than 10−4

Step-by-Step Solution:

Solution 36E

Step 1:

In this problem we need to approximate the definite integral )dx  using taylor series.

We know that  cos(x) = 1 - + -+...........

By using  the above  result , we get

Cos ( ) = 1 - + -+...........

)dx = ( 1 - + -+..........)dx

=   1 -  + - +...........

= -+-.............

= [1- - +-............] - (0)

= 1 - 0.0025 -(1.388888)+3.4722222

= 0.9974861458333

Therefore ,  )dx  = 0.9974861458333

The regular  evaluation of the integral   is 0.997486

Error ;| 0.997486 - 0.99748614583333| = 0.00000014583333 <

Step 2 of 1

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