Find the area of the region that lies inside both curves. r = 9 sin(0), r = 9 cos(0)

Q: Find the area of the region that lies inside both curves. r = sin(20), r = cos(20)

A: Consider the polar curves:  r=sin2θ,r=cos2θSolve for θ:sin2θ=cos2θ2θ=π4θ=π8 There are 8 loops for…

Q: Find the area of the shaded region in the following graph: y 2 y = sec? y = sin(4x) T/8 T/4

A: The figure is given by To evaluate : The area of the shaded region.

Q: Find the area of the region that lies inside both curves r = sin 20 r = sin 0

A:

Q: Find the exact area of the region that lies beneath the curve y = 2 sin(x), 0 < x < n.

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Q: Find the area of the region outside T= 5+5sin 0, but inside r = 15 sin 0. %3D

A:

Q: Find the area of the region that lies inside both the curves r = sin(0) and r= cos(0). A. (M В. (п…

A: This is a problem of integration. We will calculate the area by using integral method. Please follow…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r= 16…

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Q: 1. Find the area of the region that lies inside the cardioid T-1+ sin 0 and outside the circle r -…

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Find the area of the region enclosed between the curves y= sin(2x), y=0, x= 0, and x= 3n/4 (Sketch…

A: Sketch the graph and integrate function in given interval.

Q: 21. y = sin x, y = cos x, x = 0, x = 2T

A:

Q: Determine the area of the given region. y = sin x for 0 to pi/3

A: Given:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 13…

A: Given the polar curves,

Q: Find the area inside the larger loop and outside the smaller loop of the limaA§on r = 1 + cos(0).

A: Given that: r=12+cosθ The area of the curves in the polar coordinate is given by the formula,…

Q: Find the area of the shaded region shown in the graph. Ay Q y = 22 sin x 22 v = 22 cos X

A:

Q: Find the area inside the large loop and outside the small loop of r = 1 + 5 sin(θ)

A: Given, r=1+5sinθ Firstly, sketch the graph of the region to find the area.

Q: Use integration to find the area of the rose curve r = cos 20.

A: Concept: Rose curve: A rose curve, commonly known as a multiform or Grandi's rose The rose's polar…

Q: Find the area of the region that Iies inside both curves. -V 3 cos(@), r= sin(8)

A: Finding point of intersection Set up integral as A=∫αβ(rθ)2dθ

Q: Find the area of the region that lies inside both curves. r= 6 + 4 sin 0, r=6 + 4 cos 0

A: The solution is given below

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 11…

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Q: 8) Find the area of the shaded region : y = sec? x 2+ 1 y = cos X 4

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

Q: Find the area of the region bounded below by the curve y , to the left by the curve y = || cos(x)…

A: We have to find the area of the region bounded below by the curve y=12bounded to the left by curve…

Q: b) Inner loop of r = 8 – 16 sin (e)

A:

Q: 4. Find the area that lies inside the curve r = 4 cos and outside the curve r = 2.

A: Given, curves are

Q: Find the area of the region that lies inside the first curve and outside the second curve. r= 15 cos…

A: Given

Q: Find the area of the region inside the circle r=2 COS e ɑnd outside the circle r= |

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 10…

A: The required region is as follows.

Q: The area between the two curves in * the figure below is y = cos x y = sin 2x T/6 T/2

A:

Q: Find the area of the shaded region shown in the graph. Ay y = 11 sin x y= 11 cos x 2

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Q: TT 8. Find the area between the curves y = cos r and y = sin x, %3D

A: Between pi/4 to pi/2 sinx is greater than cosx  So y=sinx will be above y=cosx between pi/4 to pi/2…

Q: Find the area of the region that lies inside both curves. r = 2 + cos(0), r= 2 – cos(0)

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Q: Find the area of the shaded region in the diagram given below. y = sin(2r) 6 y = cos(x)

A:

Q: The area between the two curves in the figure below is y = cos x y = sin 2x T/6 T/2

A:

Q: 8) Find the area of the shaded region: y = sec? x 1- y = cos x 4

A: Consider the formula for the area between the curves. From the given graph, find f (x), g (x), a and…

Q: Sketch the region enclosed by the given curves and solve for the area. y = 2 cos(4x),    y = 2…

A: The given two function are y = 2cos (4x) and y = 2sin (8x).The region enclosed by the curve y = 2cos…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 1 +…

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Q: Find the area of the shaded region shown in the graph. Ay y = 27 sin x 27 y= 27 cos x

A: Solution :-

Q: Find the exact area of the region inside r = 2 sinΘ and outside r = sinΘ + cosΘ.

A:

Q: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and…

A: Given: Find the area of the “triangular” region in the first quadrant bounded on the left by the…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r= 14 cos…

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Q: Find the area of the specified region. Inside the limaçon r= 8+2 sin e

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Q: . Find the area of the region enclosed the curve x = a cos³ t, y = a sin³ t. ya a a -a 0 ·a

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Q: Find the area enclosed by the given curves y=tan(9x) and y=2 sin(9x), where -1/27 < I <T/27. You may…

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Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ),    r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: r=2a+acos 20 A r=sin 20

A: The polar curves do not intersect at any point. The area between the curves is the shaded region.

Q: . Find the area between the curves r = sin0, and r = V3cos0

A: Area of polar curve

Q: Find the area of the region that lies inside both curves. r = (3)1/2 cos(θ),    r = sin(θ)

A: Calculate the value for intersection points and the values for theta where both the value for both…

Q: Find the area of the region that lies inside both curves. r = sin(2θ),    r = cos(2θ)

A: Given: Curves r = sin(2θ),  r = cos(2θ)

Q: Find the area of the region that lies inside both curves. r = 3 + cos(0), r= 3 - cos(0) - 12 2

A:

Q: 17. Find the area of the region that lies inside the first curve and outside the second curve. r = 2…

A:

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.