Draw a left endpoint rectangle approximation of the area with n = 8. How do Ax and the change? O O If you start with only one of your eight rectangles, on the left side of your interval, and add them in one at a time, until all of the approximating rectangles are present, how much area do you add at each step? (Don't actually calculate this estimate for eight rectangles, just describe it in terms of the information you have, and explain how you would calculate it.) How is this related to Part 1 of the Fundamental Theorem of Calculus? d to the

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For this process we'll use the function f(x) = -x² + 6x - 7. You might find the following links useful:
Link to a Desmos calculator for definite integrals which displays shaded area
Link to a Desmos calculator which calculates rectangle approximations of areas
Sketch the graph of f (x), with area shaded under the curve and above the x-axis over the interval [2, 4].
Write a definite integral which represents the area of the shaded region. Don't solve it yet!
Draw a left endpoint rectangle approximation of the area with n 4 and describe what each of the following are in your
illustration:
Ax;
x for i = 1, 2, 3, 4;
. The area estimate given by this approximation. (If you use technology to compute this, explain what computations the
technology is doing.)
Draw a left endpoint rectangle approximation of the area with n = 8.
How do A and the change?
If you start with only one of your eight rectangles, on the left side of your interval, and add them in one at a time, until
all of the approximating rectangles are present, how much area do you add at each step? (Don't actually calculate this
estimate for eight rectangles, just describe it in terms of the information you have, and explain how you would
calculate it.)
How is this related to Part 1 of the Fundamental Theorem of Calculus?
Explain how each of the following are related to each other for this function, and how they are each related to the
question of how much area is under the curve over this interval. Be sure to write what each of them are.
Definite integral;
12:28
Sign out
DELL
Transcribed Image Text:For this process we'll use the function f(x) = -x² + 6x - 7. You might find the following links useful: Link to a Desmos calculator for definite integrals which displays shaded area Link to a Desmos calculator which calculates rectangle approximations of areas Sketch the graph of f (x), with area shaded under the curve and above the x-axis over the interval [2, 4]. Write a definite integral which represents the area of the shaded region. Don't solve it yet! Draw a left endpoint rectangle approximation of the area with n 4 and describe what each of the following are in your illustration: Ax; x for i = 1, 2, 3, 4; . The area estimate given by this approximation. (If you use technology to compute this, explain what computations the technology is doing.) Draw a left endpoint rectangle approximation of the area with n = 8. How do A and the change? If you start with only one of your eight rectangles, on the left side of your interval, and add them in one at a time, until all of the approximating rectangles are present, how much area do you add at each step? (Don't actually calculate this estimate for eight rectangles, just describe it in terms of the information you have, and explain how you would calculate it.) How is this related to Part 1 of the Fundamental Theorem of Calculus? Explain how each of the following are related to each other for this function, and how they are each related to the question of how much area is under the curve over this interval. Be sure to write what each of them are. Definite integral; 12:28 Sign out DELL
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