1. Graph the function f (x) = x² - 1 and show by shading the area under this curve between x = 1 and x = 3.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Let's find the area under the curve for this function f (x) = x² – 1 between
x = 1 and x =
= 3, or the integral S{(x² – 1) dx
1. Graph the function f (x) = x²
1 and show by shading the area under this
curve between x = 1 and x = 3.
2. Use the Fundamental Theorem of Calculus (Part 2) to calculate this integral.
Show steps such as antiderivative and final answer rounded to three decimals if
needed.
b-a
We use n = 5 partitions for next requests, Find Ax =
n
3. Estimate the area using the sum of rectangles from the beginning of the x
intervals or the Left-hand endpoints (L5 ). Need to show the operation, the values
of f (x;) and Ax you used, and final answer rounded to three decimals if needed.
4. Estimate the area using the sum of rectangles from the end of the x intervals or
the Right-hand end points (R5 ). Need to show the operation, the values of f (x;)
and Ax you used, and final answer rounded to three decimals if needed.
5. Use the Midpoint Rule to approximate the requested area. (M5). Need to show
the operation, the values of f (x* ) and Ax you used, and final answer rounded
to three decimals if needed.
6. Which method out of the three methods (L5 or R5 or M5) give the best
approximation. Why?
Transcribed Image Text:Let's find the area under the curve for this function f (x) = x² – 1 between x = 1 and x = = 3, or the integral S{(x² – 1) dx 1. Graph the function f (x) = x² 1 and show by shading the area under this curve between x = 1 and x = 3. 2. Use the Fundamental Theorem of Calculus (Part 2) to calculate this integral. Show steps such as antiderivative and final answer rounded to three decimals if needed. b-a We use n = 5 partitions for next requests, Find Ax = n 3. Estimate the area using the sum of rectangles from the beginning of the x intervals or the Left-hand endpoints (L5 ). Need to show the operation, the values of f (x;) and Ax you used, and final answer rounded to three decimals if needed. 4. Estimate the area using the sum of rectangles from the end of the x intervals or the Right-hand end points (R5 ). Need to show the operation, the values of f (x;) and Ax you used, and final answer rounded to three decimals if needed. 5. Use the Midpoint Rule to approximate the requested area. (M5). Need to show the operation, the values of f (x* ) and Ax you used, and final answer rounded to three decimals if needed. 6. Which method out of the three methods (L5 or R5 or M5) give the best approximation. Why?
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