Consider the function f(x) = - and the points a = 1, b = 5, and c=6. a. Find the area function A(x) = | f(t) dt using the fundamental theorem. b. Graph f and A. c. Evaluate A(b) and A(c) and interpret the results using the graphs of part (b).

Q: Find the area under the curve of y = sin x and x = 0 on the interval 0 < x < A. ! В. 1 C. D. 2

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Q: Find the area under the curve y=3x2+x+2e*/2 from x=0 to x=1.

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Q: i. Find the exact area between f(x) 7x + 10, the x-axis, x 0, and x = 5.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. (a.) Find the area bounded by the two curves; y=r+x-10 and y=-+Sx+6. i y=r-3r and y = 2-x

A: i) Given curves are, y=x2+x-10 &amp; y=-x2+5x+6 Let's draw table for y=x2+x-10 x 0 1 2 4 y -10…

Q: 10. Find the area bounded by y = x and x² – 2х — у %3D 0. -

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Q: 1. Sketch and find the area defined by y = sinh x, y = e-ª, x =0, x = 2

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the area bounded by the curves: y=-3x/(x2+2) , x2+y2=5, and x=0. This area is in the fourth…

A: The solution are next step

Q: 4. a. Use the Fundamental Theorem of Calculus to find the exact value of 3 (x3 – 4x)dx. | b. Find…

A: Solving the definite integral we have

Q: Q2. Find the area between = 0, y = e* and y = e* through the interval [-2,1]. %3D 0.6 0.4 0.2 -2.5…

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Q: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

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Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: What is the total area of the curve y T and the x-axis between I =1 and x = -1? %3D -1

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Q: a) sketch the curves of f(x) and g(x) in the same plane b) calculate the area covered by the two…

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Q: 1. Find the area bounded by the curve y In x and the %3D lines y = 0 and x = e.

A: Given curve is: y=lnx and the line y=0 and x=e Area of bounded regions: Let y=f(x) be a continuous…

Q: A Find the area bounded by y = e*, y = xe*² & x = 0.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: B) Find the total area between f(x)= sin x and g(x) = cos x on the interval [0,x)

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Q: The area under the curve between z=-1.32 and z=2.12

A: Given information- We have given 2 z-scores and we have to find the area under the curve. To find…

Q: Find the area enclosed by the loop of the curve y² = x (x - 1) ². Consider the attached graph.

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Q: et + e-* 4. Find the area of the surface generated when the function y = on the 2 interval [0, 1] is…

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Q: Find the area between y = ex and y = e2x over [0, 1].

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: Find the area of y=4ex/1+e2x bounded by the x-axis, y-axis and line    sketch the graph

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Q: Consider the function f(x) = x(x² + 3)". (a) Use the Fundamental Theorem of Calculus to evaluate |…

A: (a) Consider the given function as fx=xx2+37

Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: a. Find and graph the area function A(x) = | f(t)dt. a

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Q: Use the Fundamental Theorem of Calculus to find the area under the curve f (x) = cos xon the…

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

Q: Find the area obtain when the curve f(x) = x² - In x, for 1 <x< 3, is rotated about the y-axis.

A: Given Data The equation is f(x)=x²-1/8lnx. The interval is 1≤x≤3.   The equation of the area of the…

Q: can you please help

A: a) Plug f(x) and a=0 then integrate using the fundamental theorem of calculus.

Q: Using the fundamental theorem, find the area under the curve y = 4x3 −2x+5 and above x-axis on the…

A: Fundamental theorem: To find the area under the curve y=f(x) between x = a and x = b, simply find an…

Q: c. The area between y sin x and the x – axis for 0 < x< a

A: Area between the y=sinx and x axis from x=0 to x=π

Q: 1. Find the area bounded by y2 = 4a(y – x), y² = 2a(x + 2y – 3a) and the x-axis.

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Q: ind the area bounded by the curve y²=4x, the lines x=1 and x=4.

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Q: y = e", y = xe and x = 0

A: The region bounded by the given curve is:

Q: Q1/A: Evaluate the area under the curve y = -3x2 + 6x + 5 between x = 0 and x = 2

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Q: B) Find the area between the parabolas x = y² - 1 and x = 2y² - 2

A: Topic = Area

Q: x? Use the residues to evaluate the improper integral: -dx . (x² + 1)(x² + 4)

A: According to the given information, it is required to evaluate the improper integral using residue…

Q: Find the area between the curve y = 2(ln x)/x and the x-axis from x = 1 to x = e.

A: According to question, Given curve, y = 2ln xx

Q: P1: Calculate the area bounded by the curves: C. y = e²x and x - 2y + 5 = 0..

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Q: Find the area between the curve y = 2(ln x)/x and the x-axisfrom x = 1 to x = e.

A: Consider the given: y=2lnxxandy=0Interval 1,eFind the area:A=∫1e2lnxx-0dxA=∫1e2lnxxdx

Q: 6. Find the number a such that the line x = a bisects the area under the curve y = 1 1< x < 4.

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Q: Find the area under the curve y 2 I over the interval [1, 4]

A: Find the area under the curve y=2x over the interval [1, 4]

Q: Evaluate the integral. (Use C for the constant of integration.) t2 dt 1 - t6

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Q: Find the area under the curve y = f (x) = Vx; over the x interval [0, 8] 07 12 19

A: Sketch the region

Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: a) Sketch the curve and find the total area between the curve and the given interval on X- аxis. i)…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: y = sinx from x=0 to x=n

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Q: Evaluate the integral. (Use C for the constant of integration.) t5 In(t) dt

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Q: | (f(x) – g(x)) dx still equal to the area between the graphs of f and g if f(x) > 0 but g(x) < 0?…

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