Calculus 2

I’m studying and need help with a Calculus question to help me learn.

Hello,

Please solve with out a calculator.

Circle the final answer.

1. Find the arc length functions for y = arcsin (x) + 1 x2 with starting point (0, 1).

2. Find the exact length of the curve x = 1 y(y 3), 1 y 9.

3. An oceanographer is testing the acidity of the Atlantic ocean by placing a circular measuring device on the vertical face of the continental shelf. The measuring device has a radius of 1 meter and is placed so the top of the measuring device is exactly 125 meters below the surface.

Calculate the hydrostatic force on the measuring device. Use 1024 kg/m3 for the density of the seawater in the Atlantic ocean, and 9.81m/s2 for the force of gravity.

4. (a) Find the centroid of the region bounded by y = 1 x + 1 , y = x3, and x = 1 .

2 2 4

(b) Find the centroid of the region bounded by (x – 2)2 + (y + 3)2 = 25.

5. Find the exact area of the surface obtained by rotating the curve y = x3, 0 x 2, about the x-axis

6. Eliminate the parameter to sketch the curve:

1

x = sin θ,

2

1

y = cos θ,

2

π θ π

7. Let x = 2 t2 + 6, y = 1 t31 t.

2 3 2

  1. Find dy/dx.
  2. Find d2y/dx2.
  1. Find the length of the curve for 1 t 1.
  2. Find the area under the curve for 2 t 3

Show all work.

  1. Given the polar equation r = 1 + cos (3θ).
    1. Sketch the curve.
    2. Find the area enclosed by the curve.

2π

  1. Set up the integral for the arc length of the curve with 0 θ

(d) Find the equation for the line tangent to the curve at θ = 2π

Show all work.


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