Consider the curve described by the parametric equations x = t° +1, y= t² – º. Compute the area under the curve between t = 0 and t = 1. O 9/10 O 7/6 O 1/10 O 1/6

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Q: x= 4t³ –t² .2 y =t* + 2t² _1<t<3 4 |

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A: We have given parametric equations  xt=cos2t,yt=sin5t  for   0≤t≤π.

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Q: y = sec t, x = cosec t %3D %3D

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Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Find the arc length of the parametric curve. x=e¹, y=et, z = √2t; 0≤t≤5

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Q: b) Use the polar coordinate to find the integral S+y) dxdy

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Q: -7. х 3D sin?t, у— cos t yA

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Q: Calculate the arc length of the polar 6 sin e + 8 cos 0, 0<0<T. curve r =

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Q: Find the length of the parametric curve I = cos(t) y = 1 + sin(t) from t = 0 to t =

A: Given- x=cost and y=1+sint To Find- The length of the parametric curve from t=0 to t=π. Identity…

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A: Given: xt=-2cost  , yt=3sint , 0≤t≤π2 Formula used: The area under a parametric curve: A=∫abytx'tdt

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Q: Consider the curve Cwith parametric equations Sa(t) = t3 – 3t +1 lu(t) = t(t + 1) | lefined for t…

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Q: 36. x = sin t, y= sin t cos t, 0<t<T/2

A: Here x=sint and y=sintcost where 0≤t≤π2we have to find the area enclosed by parametric…

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Q: 1. The area under the curve with parametric equations z = 1 + t?, y = l(2 – t) in the interval 0sts1…

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Q: Find the area under the curve for the parametric function defined by the equations x(t) = t³ +t + 1,…

A: Given parametric function is  x(t)=t3+t+1 and y(t)=t2-t  where t€[1,2]

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.