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(a) Set up to nd the length of the curve given by the parametricequations
x = 1 + 3t^2; y = 4 + 2t^3 with 0 < t < 1. Do not evaluate thisintegral.

(b) Find the exact arclength of the curve given by y = x^3/3 +1/4x with 1 < x< 2.

(A question with this wording means that you do actually need toevaluate
the integral.)

please show steps for solving clearly

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Nestor Rutherford
Nestor RutherfordLv2
5 Sep 2019

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Related questions

Please answer the following with detailed explainations.

1). Find the slopes of the tangent lines to the given curves at the indicated points.

x= t^3 - t, y=t^4 - 5t^2 + 4, a) t= -1, b) t= 1, c) (0,4)

2) Find the slopes of the tangent lines to the given curves at the indicated points.

x= cos 2t, y= sin 3t, a) t= pi/2, b) t= 3pi/2, c) (1,0)

3) Sketch the graph and find the slope of the curve at the given point.

x=t^3 - t, y= t^4 - 5t^2 + 4, at (0,0)

4) Identify all points at which the cuve has a) horizontal tangent and b) a vertical tangent.

x= cos 2t, y =sin 7t

5) Find the area enclosed by the given curve.

x= tsin t, y= tcos t, from -pi/2 <= t <= pi/2

Thank you!

Show transcribed image text

The equation of the line that contains the point (1, -1, 3) and is orthogonal to the plane 2x + 3y - z = 1 is given by (a) x = 1 + 2t, y = -1 + 3t,z =3-t (b) x = 1 + t, y = -1 + 4t,z = 3 -3t (c) x = 2 + t, y = 3 + 4t,z = -1 - 3t (d) x = 1 + 2t, y = 4 -3t,z = -3 - t(note if question makes show up they are negative signs)

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