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# Midpoint Rule, Trapezoid Rule and relative error Find the ISBN: 9780321570567 2

## Solution for problem 19E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 19E

Midpoint Rule, Trapezoid Rule and relative error

Find the Midpoint and Trapezoid Rule approximations to sin πx dx using n = 25 subintervals. Compute the relative error of each approximation.

Step-by-Step Solution:

The actual value of Step 1</p>

We have to approximate using both midpoint rule and trapezoidal rule by taking n=25.

And then we have to compute the relative error for both the approximations.

Step 2</p>

Mid point rule:

The general midpoint  rule is Where the interval is and and are the midpoints for each interval.

Thus for the given question we get And the subintervals will be Therefore we have    ……….. Therefore  The relative error  in this case is given by the equation Step 3 of 3

##### ISBN: 9780321570567

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