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- Find the arc length of the curve r = cos^3 (θ/3), 0 ≤ θ ≤ π/4QUESTION 1 (a) Calculate the area of the region between the graphs of f (x) = 2x^2 + 3x and g (x) = 2x at [0, 5). (b) Determine the area of surface that is generated by revolving the portion of curve y = √14 – x^2 between -1 ≤ x ≤1 about x-axis. (c) Estimate the arc length of the graph of the function y = 2/3(x^2 +1)^3/2 over the interval [0, 1] (d) Estimate the arc length of parametric curve of: x (t) = cost, y (t) = sin t between 0≤ t ≤ πDetermine the arc length parameterization of the circle x^2+y^2 =a^2 with orientation counterclockwise and (a, 0) as the point of reference
- Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the circumference of the ellipse x2 + 2y2 = 2Calculate the arc length of the graph of g(y)=4yg(y)=4y over the interval [−6,6][-6,6]. (That is, −6≤y≤6-6≤y≤6.) Enter your answer in exact form. [Hint: it should look like A√BAB.]The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of the resulting surface.
- The arc of the parabola y = x sq. from ( 1,1, ) to ( 2, 4 ) is rotated aboutthe y -axis. Find the area of the resulting surfaceFind all of the points where the curve r = 2 cos (θ/3) intersects thecircle of radius √2 centered at the origin.The diagram shows a cone. Calculate its volume as a function of L and α using a spherical polar coordinates. Verify your answer is correct for α = 0 and in the limit α → π/2. You may wish to use figure 1.