Find the length of the curve. x = 413. y = 612. 0 sts v8 %3D The length of the curve x = 4t°, y = 6t on 0sts v8 is (Type an integer or a fraction)

Q: Given the curve r(t) = ,0stsn/2. Calculate the arc lengt O L-3 L=12 L=8 O L=3/2

A: Given curve is r→t=cos3t,sin3t and 0≤t≤π2 We have to find the arc length of the given curve. The…

Q: The position of a baseball (in ft) is represented by r(t) = 40/2 ti + (2 + 40V2t - 16t)j. Find the…

A: The arc length of a trajectory from t=a to t=b is calculated using the formula, L=∫abr'(t)dt . The…

Q: The arc length of the curve Sx=t3 ly=t? Osts1 a. 27

A: we have to solve the problem

Q: Find the length of the curve. x= 5 sint- 5t cost, y = 5 cos t+ 5t sin t, 0sts5 The length is units.…

A:

Q: Find the arclength of the curve r(t) = (6t2, 2v6 t, In t) , for 1SI58. L =

A:

Q: r(t)=(cost+t sint)i+(sint -t cost)j, a/2<15a. %3D

A: We have to find arc length of given function.

Q: What is the length of the curve arc AV543/2 r(t) = (9t)i + (6t²)j + 3 k for 0 <t< 4? (a) 130 (b) 131…

A: We have to find the arc length of the curve rt=9ti+6t2j+4543t32k for 0≤t≤4.

Q: dy d²y Find and dx dx2 x = t? + 8, y = t2 + 5t dy dx d?y dx2 For which values of t is the curve…

A: will be concave upward for all t belongs in [-1,-inf)

Q: x² : 4ay from x 0 to x = 2a

A: We have to compute the surface area of revolution of the curve x2=4ay about the y-axis between the…

Q: (e) Find the exact length of the curve. x = e cost, y = et sint, 0 ≤ t ≤n.

A:

Q: Find the arc length of the following curve. r(t) = 2t + 4 for 1sts3 The arc length is (Simplify your…

A: Given,r(t)=t2 , 423t32 , 2t+4for 1,3

Q: Find the length of the curve 7 (t) = (cos(3t), sin(3t), 2t) for – 8<t< 7 - Give your answer to two…

A:

Q: Find the arc length of the curve y = 3sin?t- 1 dt for -7<x<7. V3 28/3

A:

Q: dy dy and Find dx dx2 x = e', y = te-t dy dx d?y dx2 For which values of t is the curve concave…

A: Apply ln on both sides is x=e^t

Q: Find dy/dx and d2 y/dx2 . For which values of t is the curve concave upward? 13. x = et , y = te-t

A:

Q: Find the length of the curve r(t) = for 5 <t< 12. %3D Give your answer correct to two decimal…

A:

Q: Find the surface area generated by rotating the semi-circle x = 49 – y? be- tween -7 < y 7 about the…

A: Given, x=49-y2  between -7≤y≤7 dxdy=1249-y2-2y=-y49-y2 By the formula:  S=∫2πx1+dxdy2 Plug the…

Q: 1/B) Find the length of the cardioid 'curve: r = 1 + cose

A:

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

A:

Q: leo measure of ZY=90°, WY = 8, YX = 15, and ) resents the tangent of ZX? Submit Answer

A:

Q: Find the length of the curve r(t)= for −4≤t≤5. arc length =____?

A: We are given a curve  r(t)=&lt;7t,(t^3)/3,(14t^2)/2&gt;  we need to find out the length of arc for…

Q: The arc length of the curve r(t) = (3t², 41² ) for 1<t<6 is (a) 175. (b) 100. (c) 10.

A: Given curve  r(t)=3t2, 4t2,      1≤t≤6

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y 10x…

A: Given:

Q: Q2/Find the length of the curve r = sine + cose between

A:

Q: Find the arc length in the second quadrant of the curve x3 + y2/3 = 25 fromx = - 125 Enter the exact…

A:

Q: Round your answer to four decimal places, if necessary. Find the arc length of the portion of the…

A:

Q: 3t/2 Find the length, s, of the parameterized curve, x =3 e ° - 4t, y = 8 e 3t over the interval…

A:

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward? x = t2 + 1, y = et – 1

A: x=t2+1y=et-1

Q: nd the arclength of the curve z = t with 4 <t <7.

A: According to guidelines I am doing only first question,as multiple questions are asked.

Q: Find the radius of the osculating circle for 7(t) = (cost+t sin t)i +(sint – t cost)j +3k when t=1.

A:

Q: Quèstion 13 The arc length of the portion of the curve y = ex with 3 SxS5 is s267937.06 OA. s15.54…

A:

Q: Find dy/dx and d?y/dx2. x = e', y = te-t dx dy dx2 For which values of t is the curve concave…

A: You have posted 2 question we will solve the first question please resubmit the question which you…

Q: Find dy/dx and d'y/dx2. x = t? + 7, y = t? + 9t dy dx d?y dx2 %3D For which values of t is the curve…

A:

Q: (d) Calculate the length of the arc of the curve y=; (+1)* between the ordinates t = 0.5 andt = 2.5.

A:

Q: Find the arc length of the curve below on the given interval. 1 for 1sys2 8y2 +. 4 The length of the…

A:

Q: Q/B) Find the length of the cardioid curve: r 1+ cose

A:

Q: S2 S1 - R1– -R2-

A: We have to find arc length of S1.

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: Use the concept of derivative and apply this on formula of surface area of sphere.

Q: Find the length of the curve. Approximate your answer to 3 decimal places. r(t) = i+t²j ++t°k, [0,…

A:

Q: Find the arc length of the curve below on the given interval. 4 y for 2sys5 4 8y The length of the…

A:

Q: Find the length of the curve r(t) = for 5 < t < 19. Give your answer correct to two decimal places.

A: Given; r(t) = &lt;3cost,3sint,1t&gt;

Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

A:

Q: Find the length and the cuur vature of the Smooth eurve rCt) = (snt)i t(5 cost); + (sint)K from o to…

A: Given curve is rt→=sinti+2costj+sintk and given t from 0 to 2π We have to find the length and…

Q: 49 sec t – 1 dt with 3 Find the length of the curve x = Length is

A:

Q: Find dy/dx and d?y/dx2. x = t2 + 9, y = t2 + 5t %3D dy dx d²y dx2 %3D For which values of t is the…

A:

Q: Find the equation of the tangent to x = = VE , y = t – at the point where t = 4. Note: Sample format…

A:

Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

A:

Q: The position of a baseball (in ft) is represented by r(t) = 45 2ti + (2 + 45/2t - 16t2)j. Find the…

A:

Q: Find dy/dx and d²y/dx². x = 2 + 3, y = t2 + 3t dx d?y dx2 For which values of t is the curve concave…

A:

Q: Find the exact length of the curve (x=t?cost ly=t?sint Osts2n (n? + 4)3/2 - 4] 3 a. 4 + 4)3/2 – 1]…

A: The given implicit function is,  x=t2cost, y=t2sint0≤t≤2π

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.