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In: Advanced Math

The instructions for the given integral have two​ parts, one for the trapezoidal rule and one...

The instructions for the given integral have two​ parts, one for the trapezoidal rule and one for​ Simpson's rule. Complete the following parts.

Integral from 0 to pi ∫4sint dt

I. Using the trapezoidal rule complete the following.
a. Estimate the integral with n=4 steps and find an upper bound for

AbsoluteValueET.

T=?

​(Simplify your answer. Round to four decimal places as​ needed.)

An upper bound for AbsoluteValueET is ?

​(Round to four decimal places as​ needed.)

b. Evaluate the integral directly and find ET.

Integral from 0 to pi ∫4sint dt =?

​(Type an integer or a​ decimal.)

AbsoluteValueET =?

​(Simplify your answer. Round to four decimal places as​ needed.)

c. Use the formula AbsoluteValueET​/(true value)) times ×100 to express AbsoluteValueET as a percentage of the​ integral's true value.

?​%

​(Round to one decimal place as​ needed.)

II. Using​ Simpson's rule complete the following.
a. Estimate the integral with n=4 steps and find an upper bound for AbsoluteValueES.

S=?

​(Simplify your answer. Round to four decimal places as​ needed.)

An upper bound for

AbsoluteValueES is ?

​(Round to four decimal places as​ needed.)

b. Evaluate the integral directly and find AbsoluteValueES.

Integral from 0 to pi 4 ∫4sint dt=?

​(Type an integer or a​ decimal.)

ES=?

​(Round to four decimal places as​ needed.)

c. Use the formula AbsoluteValueES​/(true value)) times ×100

to express AbsoluteValueES as a percentage of the​ integral's true value.

? ​%

​(Round to one decimal place as​ needed.)

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Solutions

Expert Solution

Colby Messinger answered 1 year ago
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