If the area enclosed by the curve x = 5 cos³ t and y = 5 sin° t (where t E R) is A, then what is A? 8

Q: find the length of the indicated portion of thecurve.r(t) = (et cos t)i + (et sin t)j + etk, -ln 4…

A: Given, r(t)=etcosti+etsintj+etk length L=∫-ln40r'(t)dt            .......(1) now derivate given…

Q: A. Find the area enclosed by each of the following curves. T= 4 sin e

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Q: Find the area between the two curves in the following figure: r=2a+a cos 20 r=sin 26 For a = 16…

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Q: Find the area in the first quadrant that is inside the circle r = 4 sin 0 and outside the lemniscate…

A: We need to find area.   NOTE - As per our guidelines we can solve one question so please upload…

Q: . The area of the region that lies inside the cardioid curve r = cos 0 + 1 and outside the circle r…

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Q: The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab…

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Q: Calculate the length of the side XY given the following data for 29°: Sin 29° = 0.485 Cos 29° =…

A: Solve for xy

Q: Question ): The integral that represents the length of the curve y = tan(2a), where <a <, is the…

A: Given y=tan2x

Q: In the given equation as  follows ,find the area of the region :-  see the equation as attached here…

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Q: The area of the region inside the circle r= 6 cos e and outside the cardioid r= 2(1+ cos 6), a > 0…

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Q: The approximation of I = S, cos x? dx using composite Simpson's rule with n 3 is: -1.5412 O This…

A: Formula :     The formula for composite simpson's rule is     ∫abf(x) dx ≈∆x3 [fx0 +4 fx1+2fx2+4…

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: Find the area of the region inside r = 9 cos 0 and inside the rose curve r= 9 sin 0

A: Area between the polar curves

Q: Given that xs an auite angleand cos x = 3/4 , ind the exac valne d fan

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Q: Find the length of the following curve at the given distance. Rie). cos'e ?a sin? t } Cos t i 2

A: Given curve is R→t=cos3ti^+sin3tj^ where 0≤t≤π2. We have to find the length of the given curve at…

Q: If the area enclosed by the curve x = 4 cos³ t and y = 4 sin t (wheret e R) is A then what is A?

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Q: If the area enclosed by the curve a = 7 cos t and y = 7 sin t (where t e R) is A, then what is A?…

A: If the area enclosed by the curve x=7cos^3t and y=7sin^3t (where t∈R) is Aπ8, then what is A?

Q: 7. In 00, the diameter BS L PA a. If DS = 1 cm and BS 10 cm, find a.1. OD a.2. OP b. If OA = 12 cm…

A: Here we have used several theorms as per mention

Q: - T If the area outside the cardioid r = 6 – 6 sin 0 and inside the circle r = 6 is A - , then what…

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Q: 4.) Find the area inside the circle r=v2sin (0) and the lemniscate r2 = cos(20)

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Q: 5 sin t (where t e R) is A, then what is A? %3D If the area enclosed by the curve x = 5 cos³ t and y…

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Q: If the area of APQR is A, give the expressions that complete the equation for the measure of ZR. R…

A: We will use formula for area of triangle.

Q: The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Given the integral J sec° (x – 1) tan" (x – 1)dx, which of the following equations will be useful…

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Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

A: Solution:-

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: If the area enclosed by the curve z = 5 cos t and y = 5 sin' t (where te R) is A- then what is A?…

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Q: 13.2. Find the length of the arch of the cycloid given by z(t) = a(t – sin t) + a i(1 – cos t), 0 <t…

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Q: If the area inside the cardioid r = 6 – 6 sin 0 and outside the circle r = 6 is T+ 8 A · then what…

A: To solve the following problem

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

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Q: Find the area inside of the cardioid r = 3(1+ cos(4)) and outside of the circle r = cos(4). a)13m b)…

A: Given problem is :

Q: Given the following figure below. What can not be proven? 1. CX =DX root 3 2. CD is perpendicular…

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Q: Evaluate cos dV, where E is the region enclosed by the E sphere p = cos(4).

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Q: Find the area of the interior of r = 6 sin 0. Find the area between the loops of r 1+2 cos 0. Find…

A: Let's find.

Q: Given R(t) =4 cos ti + (1 + 3cost)j + 5sintk. Find the arc length of the portion of R(T) from t = 0…

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Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

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Q: Find the area of the specified region. Shared by the circles r=D 3 cos 0 and r= 3 sin 0

A: Consider the given circles r=3·cosθ and  r=3·sinθ To find the area of the region first find the…

Q: Find the areas of the regions Inside the circle r = 3a cos θ and outside the cardioidr = a(1 + cos…

A: Given: The regions Inside the circle r = 3a cos θ and outside the cardioid r = a(1 + cos θ), a &gt;…

Q: Find the area of the specified region. Shared by the circles r = 8 cos(e) and r = 8 sin(8) %3D A)…

A: Given :   r = 8 cos ( θ )   r = 8 sin (  θ )

Q: A curve in spherical coordinates x' for the line element ds? = (dx')² + (x')²(dx²)² +…

A: To Find the arc length to use the formula

Q: Find the area of one leaf of the "four-petaled rose" r = 5 sin 20 shown in the following figure: y…

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Q: Find the area Inside the lemniscate r= 6 cos 20 and outside the circle r= v3. Inside the lemniscate…

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Q: Find the area inside the larger loop and outside the smaller loop of the limicon ? = 1 + 2 cos ?.

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Q: (1) Find the area of the hypocycloid F (t) = (cos³ (t), sin® (t)), te [0, 27].

A: Given The given hypocycloid is r¯=cos3t,sin3t, t∈0,2π. Apply formula A=∫D∫dA=∫Cx dy+0 dx=∫Cx dy

Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

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Q: If the area enclosed by the curve r = 2 cos t and y = 2 sin t (where t E R) is A- then what is A? 8.…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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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.