By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum, and accurately illustrate the curve using graphs.

Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

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Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Find the area of the region bounded by the parabola y=5x^2, the tangent line to the parabola is at…

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

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Q: Find the area bounded by the parabola x²=8y and its latus rectum.

A: To find: The area bounded by the parabola x2=8y and its latus rectum: Concept used: Area under the…

Q: By sketching the graph and using integration, find the area of the region bounded by, p*y² = x°(2P –…

A: P4y2=x5(2P-x) To Find: Sketching the graph and using integration, find the area of the region.

Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum.

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Q: Find the area of the region bounded by the parabola y = 3x2, the tangent line to the parabola at (3,…

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Q: π Find the area of the region enclosed by y = sin¯¹(x), y = and the y-axis without using integration…

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Q: I. Find the area bounded by the curves y=x', y 1, and x = 0 using double integration.

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Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

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Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

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Q: rea of the region enclosed by

A: we have to find the area of the region bounded by the curve, y=2-x2 .....(1) and the line y=-x

Q: Apply trapezoidal and Simpson's rules to the integral

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Q: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: If we want to find the area between the curves x = −y 2 + 1 and x = y 2 − 1, shall we integrate with…

A: Given curves are x=-y2+1 and x=y2-1

Q: Find the area bounded by the curves y = x³, y = 1, and x = 0 using double integration.

A: Area of the required region is 3/4 see below the calculation

Q: Find the area under one arch of the cycloid x = a(t-sint) , y = a(1-cost)

A: Introduction: A cycloid is a two-dimensional curve that is constructed with half circles. One arc of…

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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Q: Find the area bounded by the ,3 curves y = x°, y= 1, and x using double integration.

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Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

Q: Find the area bounded by the parabolas y = 6x - x2 and y x- 2x. (Round answer to three decimal…

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Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In x lying…

A: Solution We have to find the Surface area generated by revolving about the y-axis the part of curve…

Q: Find the area bounded by the given curves. v = 6x² – 16x – 7 and y = 3x2 + 2x – 22 | square units

A: Given curves are: y=6x2-16x-7y=3x2+2x-22

Q: Find the area of the region bounded by the parabola y=x2 , the tangent line to this parabola at…

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Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

Q: Find the area of the region bounded by the parabola y = 2x2, the tangent line to the parabola at (3,…

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine its area…

A: Sketch the bounded region.

Q: Prove by using integration by change in variable the ff. integral: dx = arcsec x +C xVx² – 1

A: Our Aim is to prove the given integral given below by using change of integration.∫dxx(x2-1)dx -(i)

Q: By Stetching the graph and using integration, Find the area of the region bounded by, 25 y = x…

A: Given  25y2=x210-x.

Q: Find the area bounded by y = x² −1, the x axis, and x = 4 in the first quadrant using 6 divisions of…

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

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Q: 2. By integration, show that the area of a circle of radius r is A = rr?

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: For Trig integration find the integral of  Sec^6(6x)

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Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: Sketch the region enclosed by the curves 4x+y2=12 and y=x then find its area using the appropriate…

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = =9y-y2 and y = 2

A: Follow the steps.

Q: First make a substitution and then use integration by parts to evaluate the integral. dx

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Q: x³ – 6x2 + 8x, and y = x² – 4x - -

A: Given curves, y=x3-6x2+8xandy=x2-4x To find the area bounded by above curves using vertical strips.

Q: Evaluate the integral. Use C for the constant of integration. 4dx

A: Given integral is- I=∫4dx9x3 It can be written as- I=49∫1x3dx=49∫1x32dx=49∫x-32dx

Q: Find the area bounded by the curves y = x3 , y = 1, and x = 0 using double integration.

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…