I. Integral Evaluation. (40 points) Evaluate the following five integrals. | (5z* - 8z + 6z) dr. 1. 25 1 dr. 2. */4 3. secr tan z dr. da. +1 4. 4x3 dr. 5. 14 +1

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: d the area bounded by the graphs of the indicated equations over the given interval (when stated).…

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Q: Use the Addition Property for integrals and the results of Section 5.2 to find values for r and s.…

A: We have to find the value of r and s.

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

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Q: 8. Find the area bounded by x² – 6x + y = 0, - x² – 2x – y = 0, and the x – axis.

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Q: (b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curve by rectangles,…

A: Given function is f(x)=1x, for x≠01,   for x=0 Given interval [-1,1] Now we have to divide the…

Q: Identify the method applicable and evaluate the integral using the identified method: adx 5. S -…

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Q: Q3/Find the value of integral along the curve C joining the points (1, 1) and (2, 3) | (12z2 – 4iz)…

A: We have to find the value of integralalong the curve C joining thepoints (1, 1) and (2, 3).

Q: 10. Find the area between y = 3x²+14 and y = 4x + 2 over the interval [-2 , 2]

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Q: Find the area between the curves. y = x2 − 2x + 7 and y = x2 + 8 from x = 0 to x=6

A: Let fx=y=x2-2x+7 and gx=y=x2+8. First, we will find the intersection point of both the curves…

Q: Find the area under the curve y = - over the interval [4, 9]. (4x + 2)² Enter the exact answer. area…

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Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: Find the survace area of revolution about the x-axis of y= 4sin(2x) over the interval x is greater…

A: Given: The curve y=4sin2x for 0≤x≤π2 To find: Surface area of revolution of given curve about…

Q: 7) (g) Set up and evaluate the definite integral for the area of the surface generated by revolving…

A: we use integration formula for area of surface rotating about x-axis..

Q: The area bounded by the small loop of the line limaçon r= 1-2sintheta is given by the definite…

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Q: Find average Value of f(x)=X³ on [1,2]. Then find Point CE [1,2] meun € [1,2] quaranteed by the…

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Q: 1. Find the area in the second quadrant bounded by the curve 2x² + 4x +y = 0 using two methods

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Q: f(x) = avbx – c %3D the x -axis and the line x= 15 using Right Riemann Sum with 6 equal intervals if…

A: To calculate the area of the region bounded by the function fx on the interval a,b by the right…

Q: f(x) = x^2 − 3x + 2 and the line g(x) = x − 1 over the interval [0,2] .

A: Being bounded means that one can enclose the whole graph between two horizontal lines.

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

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Q: Using Integration by Parts, the integral [(x8. is equal to x10 5 - the above + 2x⁹) In x dx…

A: Given: I=∫x8+2x9lnxdx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: Use a table of integrals to find the length of the curve y = x² from x = 0 to x = 2. %3D

A: The equation of the curve is given as, y = x2 we need to find the length of curve in the interval x…

Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: Set up an integral that represents the surface area of the surface generated by revolving the graph…

A: Given problem :- Set up an integral that represents the surface area of the surface generated by…

Q: Find the area of the region bounded by el MQ4.3.png f (x) — aVbx — с the x -axis and the line x = 13…

A: Given fx=abx-c where a=4.1, b=4, c=6

Q: The area between the curves y =2 cos (x) + 4 and y = 2 – 2 cos (x) on the interval [0, 1] is: 27 3 3…

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Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

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Q: Set up the integral used to find the length of the curve y = V1-25 on the interval -<zs Select the…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12-2²…

A: we have to find out area

Q: The area of the region bounded by the curves y =x and y = 20–x² is попe 4.4 O 4= " |20–x²-x| dr -4.4…

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Q: By making an appropriate change of variables, evaluate the double integral -y², I = || ( + y)e* v°…

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Q: Find the area under the curve 3 over the interval [3, 8]. y = (4x + 2)² Enter the exact answer. area…

A: y = 34x+22,interval : 3, 8

Q: Find the area under the curve y = - - over the interval [4, 9]. (4x + 2)² Enter the exact answer.…

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Q: ii) area bounded by x -y = 1, 2x + y = 5and x + 2y = 7 in first quarter is: 20T 21T 22m

A: The area is the measure of the amount of space occupied by the plane figure. It is measured in terms…

Q: a) Evaluate the Integrals: 2x2 + 3 x(x + 1)2 b) Find a horizontal line y = k that divides the area…

A: (a) part Consider the given integral ∫2x2+3xx+12dx Now,…

Q: 5. Determine the area below f(x) = 10 - 2x² and above the line y = 3. 6. Determine the area bounded…

A: Given problem:- Determine the area below f(x) = 10 - 2x2 and above the line y = 3

Q: Can i get help step by step?

A: We graph y=7x using a graphing calculator  The graph cuts  x-axis at x=0  So over the interval…

Q: Set up an integral for the length of the curve. y = Vi-x7, -sxs 1/4 4+ 49, 12 dx -1/4 4- 4x7 + 7x6…

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Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

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Q: ROBLEM 1: Evaluate the integral ,(1 – x – 4x° + 2x*) dx a) Analytically b) Single application of…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the area under the curve over the indicated interval. [4.3] y = 4 – x²; [-2,1] y = x + 2x + 1;…

A: Please refer the attached image for complete solution.

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: Evaluate the integral 8(x – 9) J (x + 5)(x – 2) ** Note: Use an upper-case "C" for the constant of…

A: Solve by substitution and simplify.

Q: Find the area under the curve y = over the interval [4, 7]. (4x + 3)2 Enter the exact answer. area =

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Q: 4. Express the integral as an equivalent integral with the order of integration reversed. 2√x (a) ff…

A: The process of switching between dxdy order and dydx order in double integrals is called changing…

Q: Set up and evaluate the definite integral for the area of the surface generated by revolv y = 1x3 dx…

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Q: Compute , F - dS for F = (sin(y), sin(z), yz), S being the rectangle 0 < y < 3, 0 < z < 6 in the…

A: Given that, F=siny, sinz, yzThat is,F=(siny)i+(sinz)j+(yz)k Evaluate: ∫∫SF.dS

Q: Find the area of the region bounded by the graphs of the equations: f (x) = sin x, cos 2x where -<x<…

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Q: (ii) Calculate the iterated integral by first reversing the order of integration. S. St yer² 0 Vy x3…

A: Given double integration ∫01∫y1 y ex2x3  dx dy