(a) Find ALL of the points where the following curves intersect; (r- 3)2 2 4r 2 = 1+ Y3 = 6-r (b) Using a well proportioned and neatly drawn graph of these three curves, identify the area which lies above y1, and below y2 and below y3- (c) Using integral calculus, calculate the area defined in part (b) of this question.

Q: 3) Show that the area of the shaded parabolic arch y = (x-a)(b-x)in the figure is equal to…

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Q: 11. Find the area bounded by the curve 5y²-16x and the curve y²=8x-24. A. 30 sq.units C. 16 sq.units…

A: We need to find area bounded by curve.

Q: 2. Sketch the curve y=3x2+1 between x=-2 and x=4. Determine by integration the area enclosed by the…

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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 & y=-x2+5x+6 Let's draw table for y=x2+x-10 x 0 1 2 4 y -10…

Q: Solve the area covered by the x-axis and f(x) = e^x from x= 1 to x = 4 with interval h = 0.25 using:…

A: ∫abf(x)dx≈Δx(f(x0+x12)+f(x1+x22)+f(x2+x32)+⋯+f(xn−2+xn−12)+f(xn−1+xn2)) Mid point rule and…

Q: 9. Find the area of the region that lies inside both curves * r = 2 sin(0) and r = 2 cos(0) O -1 27…

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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: 7. Consider the cardioid r = 2-2 sin0 and the circle r 2 as shown on the right Set up, but do NOT…

A: Consider the cardioid r=2-2 sin θ and the circle r=2 as shownSet up, but do not evaluate, the…

Q: d the area of the region that lies under the given curve. Round your result to the nearest…

A: The question is taken from the calculus in which we have to find the area under the given curve so…

Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) %3D and r = 4 cos(0) 2л -…

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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: What is the area of the region bounded above by y= sin x below by y=x- T and from the left by the…

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Q: 1+x² 1. Find the area of the region bounded by the curve y=- and the lines y = 0, y = x, x = 2. 2x2

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Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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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: 2. Sketch the curve y=3x²+1 between x=-2 and x=4. Determine by integration the area enclosed by the…

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Q: 2. Find the area bounded by the curves y² = x and x = 2y – y² as shown. x = 2y – y? -y² = x ( 1,1)…

A: given ,

Q: 1. Find the area of the region bounded above by the curve y = 2e-* + x, below by the curve y = , on…

A: We have to find out the area of the region bounded above by the curve   y = 2e-x + x , below by the…

Q: 4- Find the area of the region bounded by the curves y - 3x = 4 and 3r – 2y = 11. a) b) e) d) e)

A: The equation of the curves are : C1 :  y2-3x = 4  ⇒ x = y2-43 C2 : 3x-2y = 11  ⇒ x = 2y+113 To…

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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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: 1. Find the area bounded between the curves: y = x°, x = 1, and y -8

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Q: 1. Find the area under the parabola y = 8 – x 2 – 2x, above the x-axis.

A: Given parabola y=8-x^2-2x Area = double integral (dx dy). First we will draw the graph based on…

Q: The area bounded by the curve y = 2x - x and the ordinates x =0;x= 4 is: %3D %3D 14 sq. units 3 15…

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Q: S(x) = }x³ + d [1/V2, 1]

A: SINCE YOU HAVE ASKED MULTI PAL QUESTION IN ONE REQUEST SO WE WILL BE ANSWERING ONLY FIRST QUESTION.

Q: 7. The integral used to find the length of the curve y=xbetween x = 0 and x = 4 is (Circle your…

A: I have Provided this answer in step-2.

Q: Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT:…

A: Given  x3 x2 + 2xy - y2 =0 x3 = (y - x )2 x3/2x = y      and   y = -x3/2x   AREA = ∫x1x21f(x)-g(x)dx…

Q: 31. Find the area bounded by the parabola y-3x +3 = 0 and the line x 4. %3D y-axis X-axis 1

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Q: 1. Find the area bounded by the parabola x² – 2y = 0 and x² + 2y = 8. %3D

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Q: 2 - y², y = − sin (727), and Let R be the region below enclosed by the curves x = x = -1, as shown…

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Q: 4/2 x2 -1 for [0, 1]. Find the length of the curve y=- Find the area of the curve bounded by the…

A: (7)We will find the length of the curve.

Q: f(x) = }x* + [1, V2]

A:

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: Find the area bounded by the curve y = x2(x – 3) and y? + 8y – 16x + 48 = 0. Show complete solution…

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Q: 1. Find the area between y=x and y=x' fromx=-1 to x-1. 2. Find the area of the "triangle" region…

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Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

Q: 15. What is the appropriate total area bounded by the curve y = sin x and y = 0 over the interval 0…

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Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Q9// From x = -3 to x = 1, sketch and find the area of the region bounded by the curve x = F/y+ 4…

A: Given: To Find:

Q: (a) Find the total area of the region between the curves y = sin x and y = cos x for 0 < x < 3x/2.…

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Q: a)Find the surface area of the volume generated when the curve y = x revolves around the x-axis from…

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Q: a. Set up an integral for the length of the curve. b. Graph the curve to see what it looks like. c.…

A: Explanation of the answer is as follows

Q: 1/ Find the area of the region enclosed between the curves y= 2r'+10 and y=4x+16 and x=-2 and x=5?…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y – T = 2 and I = 4. In…

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Q: - x² + 8x between = Use the Fundamental Theorem of Calculus to find the "area under curve" of y x =…

A: Sol:- Area under a curve definitionThe area under a curve is the area between a curve fx and the…

Q: The rectangle shown here has one side on the positive y-axis, one side on the positive x-axis, and…

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Q: 1- x Find the area of the region between the curve y = 2- 0 < x < 1, and the x-axis. p2 1 1'

A: here we have ................x-axis ................given interval