The following for an integral ∫ 1 3 ( − 2 x + 7 ) d x . a. What area does the integral represent?

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Answer 1

Question

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…

5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈

2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch It

Answer 2

Question

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Answer 6

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

Answer 7

Chapter 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

Answer 8

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

Answer 9

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

Answer 10

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Answer 11

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

The following for an integral ∫ 1 3 ( − 2 x + 7 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how the integral represents an area under the graph of 2 x + 7 from 1 to 3. Provide a graph that illustrates this area.

Concept explainers

Videos

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

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Chapter 14 Solutions

Additional Math Textbook Solutions

The following for an integral ∫ 1 3 ( − 2 x + 7 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how the integral represents an area under the graph of 2 x + 7 from 1 to 3. Provide a graph that illustrates this area.

Concept explainers

Videos

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . a. What area does the integral represent?

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . b. Provide a graph that illustrates this area.

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . c. Use a graphing utility to approximate this area.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.