The instructions for the given integral have two? parts, one forthe trapezoidal rule and one for? Simpson's rule. Complete thefollowing 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 toexpress AbsoluteValueET as a percentage of the? integral's truevalue.

??%

?(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 forAbsoluteValueES.

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'strue value.

? ?%

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

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