The area of the region outside the curve r-2+2sin0 and inside the curve r-6sin0 is given by which integral below

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: Sketch the region whose area is given by the definite integral. 36- х2 dx -6-

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Q: Find the area A of the region that is bounded between the curve f(x) = -2 sin () and the curve g(x)…

A: Given that we have to find the area of the region that is bounded between the curve f(x)=-2sinx4,…

Q: Use a double integral to find the area of the region. The region inside the circle (x − 3)2 + y2 =…

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Q: Find the area of the region enclosed by the curves y - 2x =7 and x - y= 4. Set up the integral that…

A: Answer and explanation is given below..

Q: 3. Find the area bounded by the curve 2x² + 4x +y = 0 and y = 2x. Answer: 'n bs

A: Given:     curve 2x2+4x+y=0                and y=2x    2(x2+2x+1)=-y+2(1)    2(x+1)2=-(y-2)…

Q: 16-y2 16 – 22-y drdy by using appropriate coordinate system. an

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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: Find the area of the region bounded by (enclosed by) y = x² + 5x and y = 5x + 4 Be sure to a) graph…

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

A:

Q: What is the area under the curve of f(x) = 4 from r = 2 to r = 6? %3D

A: To find the area under the curve of f(x) = 4 from x = 2 to x = 6 Area = ∫26f(x)dx

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(æ) dz…

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Q: Find the area of the region that bounded by r=1- cos(0)

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Q: use a double integral to find the area of the shaded region.

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Q: a) Use Trapezoidal and Simpson's Rule to evaluate the integral , (2x – 1)dx by taking n=4

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Q: Write a definite integral which computes the area of a surface of revolution 3 1 from rotating y=-x²…

A: Topic- Application of Integration

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: 1/ Find the area of the region enclosed between the curves y= 2r²+10 and y=4x+16 and ,x=-2 and x-5?…

A: Given          y=2x2+10    and  y= 4x+16,   x=-2 and   x=5.

Q: Can i get help step by step with this problem?

A: Given,

Q: Use the Trapezoidal Rule to approximate the given integral with n= 6. Show your work 1 dx

A: Topic- Integration

Q: Use the Trapezoid Rule to approximate the area under the curve f(x) = 2x° + 1x – 3 from x = x = 11.…

A: Use trapezoidal rules

Q: Use a definite integral to find the area of the region between the curve y = 16x and the x-axis on…

A:

Q: Approximate the area under the curve y=4x2+1 on the integral [0,4] n=4 using the trapezoid rule

A: Given : y = 4x2 + 1  To find : Area under given curve using trapezoid rule . Solution : Approximate…

Q: Use a definite integral to find the area of the region between the curve y = 17x and the xX-axis on…

A: Area is the double integral with respect to y and x. It is known that at x-axis that is y=0. We have…

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: Use a definite integral to find the area of the region between the curve y = 6x and the x-axis on…

A: Given the curve y=6x. We need to find the area of the region between y=6x and the x-axis on the…

Q: Find the area bounded by y = x³ and y = x² + 2x on x € [-1, 1]. Submit your answer in fractional…

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Q: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

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Q: 8. Sketch the region enclosed by the curves: y = x² – 1, y = 7 – x². Then set up (but do not…

A: Given- y=x2-1 and y=7-x2 To Sketch- The region enclosed by the above curves and then set up the…

Q: Q4] Use double integrals to find the area of the region that lies inside the cardioid r 1+ cos 0 and…

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Q: Use a double integral to find the area of the shaded region. n/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5…

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Q: What is the area under the curve of f(x) = 4r from r = 2 to r = 6? %3D

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Q: Find area bounded by the circle x^2+y^2=25, the y-axis and the parabola y=6x-x^2 using iterated…

A: Given : Circle : x2 + y2 = 25, Parabola : y = 6x - x2   To find : Area bounded by the given curves…

Q: Use a definite integral to find the area of the region between the curve y = 3x and the x-axis on…

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Q: The area bounded by the small loop of the limaçon r = 1 – 2sin0 is given by the definite integral

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

A: To find the area:

Q: Find the area under the curve y 5 -over the interval [4, 7]. (3x + 1)² Enter the exact answer. area…

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Q: Find the area between the curve y = 2x² + 4x-6 and the x-axis from x = -2 to x= 3. %3D %3D %3D

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Q: Sketch the region bounded by f (x) = 3+ 10e¬2ª, g(x) = 3+2e", x = -1 and x = 1. Using calculus, find…

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Q: Find the area between the curve  y = x2 + 10x + 16  and the x-axis from  x = −2 to x = 1.  (Give…

A: To find the area between the curve y=x2+10x+16 and the x-axis from x=-2 to x=1. This is given by…

Q: Use the substitution formula to evaluate the integral. the integral from 0 to pie/2…

A: To  Determine:Use the substitution formula to evaluate the integral. Given: we have an integral…

Q: Sketch the region whose area is represented by the definite integral. dx 2 4 Use a geometric formula…

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Q: Find the area under the curve f(x) = x° on x =[- 2.5, 5.5] using the Midpoint Rule with n = 8

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Q: Find the approximation of the area under the curve using 4 trapezoids. Use the function y = x2 - 4x…

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Q: Find the area of the region Cut from the Ist auadrant /2 r= 4(2-Sin 20) by the curve

A: Solve for the area

Q: Approximate the area under the curve f(x)=sin2(πx) using the midpoint approximation rule with 3…

A: Using a sum of midpoint rectangles calculated with the given formula

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

A: This question can be solved using the concept of integration by substitution.

Q: 65 Use the midpoint rule with 8 rectangles to approximate In 65 dx: (F),7 The integral is…

A: To find the approximate value of ∫1651xdx Using mid point rule Given n=8

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.