Find the between the two curves. area 2. X=ay, a'y=x 3

Q: x² cos²y – sin y = 0, (0, ) re (a) tangent and (b) normal to the curve at the given

A:

Q: Find the area between the inner and outer ovals of the curve r2 = 16(2 – cos 0)

A: Given,

Q: Given xy + cos(xy) + 3x = 1, answer the following: Write the equation of the normal line to the…

A: Given,            xy + cos(xy) + 3x =1

Q: 6. Find the length of the curve r = 1+ cose

A:

Q: Find the area between a large loop and the enclosed small loop of the curve  r = 4 + 8 cos(3θ).

A:

Q: 3 The arc length of the portion of the curve y =x² with 0<x<4 is

A:

Q: Find the area of the region that lies inside the curve r = 2 + cos (2a), but outside the curve r = 2…

A: The given curves are r = 2 + cos (2a), r = 2 + sin(a). Use online graphing calculator and sketch the…

Q: find the arc length of the curve on the given interval y = (x2+2)3/2/3 on [0,1]

A: Given curve is: y=(x2+2)323 from x=0 to x=1Heredydx=32(x2+2)12×2x3=xx2+2

Q: Find the length of the curve. x = cos t y = sin t

A:

Q: Find the length of each of the following curves: %3D %3D x (ey + e) from y = 0 to y = 1

A: The length of a curve means the arc of the length of a curve. The arc of the length of a curve in…

Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

A:

Q: Given xy + cos(xy) – 4x 5, answer the following: Write the equation of the normal line to the curve…

A:

Q: Find the area between the inner and outer ovals of the curve r2 16(2 – cos 0)

A: To find the area between the inner and outer ovals of the curve

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: 1) Find the length of the curve; y = e" from r= 1 toI = 2.

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

A:

Q: Find the arc length of the graph of the function over the indicated interval. x = = + 2)/2, osys7…

A:

Q: Find the area of the curve: r² = 16 cos 20

A:

Q: When the radius r of a sphere increases with time t, the change in area dA is dt Оа. 4 3 O b. dr 8n…

A: We will find the change in area with time as following.

Q: Done Find the area between a large loop and the enclosed small loop of the curve r = 4 + 8 cos(30).…

A:

Q: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê

A:

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

A:

Q: 2. Find the length of the curve 1<t<4. given by r= e'(sin t+cos t), y = e'(cos t-sin t), OS

A:

Q: 3/ 10. Find the arc length of the curve y = x/2 +4 from x = 4to x = 9.

A:

Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

A:

Q: Find the area of the surface generated when the given curve is revolved about the y- axis. y =, for…

A: Answer is optional B

Q: 1 dx , by taking n=4. Inx A. Use Simpson's rule to evaluate B. Find the length of the curve y = x2…

A:

Q: 3 The arc length of the portion of the curve y=x 2 with 0<x<4 is

A: I have append the formula used to find arc length in the solution part.

Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

A:

Q: 10. Circles tangent to the x-axis. Amm. [1+())- [yy +1+(.

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: What is the area of:  To the right of Z = 0.29 and to the left of Z = -1 Show the solution and…

A:

Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

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: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

A:

Q: Find the arc length of the graph of the function over the indicated interval. X = 3 Vyv - 3), 1<y s…

A:

Q: Find the required x-value. For a x2-cu -curve with 27 degrees of freedom, find the X-value having…

A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1 + 2 cos(30).…

A: (1).    The given curve is: r=1+2cos3θ

Q: Find the equation of the line that is normal to the curve x cos(xy² – y) = (x + y)² at the point…

A: here option c is true

Q: AT is tangent to oG. 8 10 Find: AN. AN = %3D units

A:

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

A:

Q: Find the exact length of the curve. y = In(cos(x)), 0 s xs- TO 6. Need Help? Read It

A: Given problem:- Find the exact length of the curve.   y = In(cos(x)),   [0, π/6]

Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…

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.