a) Evaluate the integral exactly, using a substitution in the form œæ = sin 0 and the identity cos? a = } (1+ cos 2æ). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in æ®. Give the coefficient of æ* in your expansion: c) Integrate the terms of your expansion and evaluate to get an approximate value for the integral. Enter the value of the integral: d) Give the percentage error in your approximation, i.e. calculate 100×(approx answer - exact answer)/(exact answer). Enter the nercentage error:
a) Evaluate the integral exactly, using a substitution in the form œæ = sin 0 and the identity cos? a = } (1+ cos 2æ). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in æ®. Give the coefficient of æ* in your expansion: c) Integrate the terms of your expansion and evaluate to get an approximate value for the integral. Enter the value of the integral: d) Give the percentage error in your approximation, i.e. calculate 100×(approx answer - exact answer)/(exact answer). Enter the nercentage error:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Question
Transcribed Image Text:The integral o" 6y1 – 9x? dr is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.)
a)
Evaluate the integral exactly, using a substitution in the form ax = sin 0 and the identity cos² ¤ = ; (1+ cos 2æ).
Enter the value of the integral:
b)
Find the Maclaurin Series expansion of the integrand as far as terms in æº. Give the coefficient of * in your expansion:
c)
Integrate the terms of your expansion and evaluate to get an approximate value for the integral.
Enter the value of the integral:
d)
Give the percentage error in your approximation, i.e. calculate
100x (approx answer - exact answer)/(exact answer).
Enter the percentage error:
%
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