Need Help? ad I ster It lo se the Trapezoidal Rule and Simpson\'s Rule to approx

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Need Help? ad I ster It lo se the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. the exactvaleofthedefiniteintegriniteitegralforthe />de, n-5 x' dx, n 6 Exact Trapezoidal Simpson's Need Help?Read Talk to a Tuter Low Disk Space We need more space to install important updates. Select Fix issues to get started 3 points LarCalc11 8.6010 Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given decimal places and compare the results with the exact value of the definite integral. Type here to

Explanation / Answer

Integrate x^3 to obtain x^4/4

Hence

exact =(1/4)(7^4 -1^4)

=600

==============

?x = (7 - 1)/6
?x = 6/6
?x = 1

Trapezoidal=(1/2) * (1) * ( f(1) + 2*f(2) + 2*f(3) + 2*f(4) + 2*f(5) + 2*f(6) + f(7) )

=(1/2) * (1) * ( 1 + 2*8 + 2*27 + 2*64 + 2*125 + 2*216 + 343 )

=612

=============

?x = (7 - 1)/6
?x = 6/6
?x = 1

Simpson =(1/3)* (1) * ( f(1) + 4*f(2) + 2*f(3) + 4*f(4) + 2*f(5) + 4*f(6) + f(7) )

=(1/3)* (1) * ( 1 + 4*8 + 2*27 + 4*64 + 2*125 + 4*216 + 343 )

=600

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