Surface area calculations Use the method of your choice to determine the area of the surface generated when the following curves are revolved about the indicated axis.
24.
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- 42) Find the surface area of the solid that results when the region in the first quadrant bounded by the curve x2 + y2 = 72 from x = 2.9 to x = 7 is revolved about the x-axis. Express your answer in 3 decimal places.arrow_forwardfind the surface area of the curve x=cos^2(y) on the interval (0 <= y <= pi/2) rotated about the y-axis only HANDWRITTEN answer needed ( NOT TYPED)arrow_forwardnder what conditions can you find the area of the surface generated by revolving a curve x = ƒ(t), y = g(t), a … t … b, about the x-axis? the y-axis? Give examples.arrow_forward
- Find the surface area generated by revolving about the x-axis the curve y = 2(15-x)^1/2, from x = 5.32 to x = 10.28arrow_forwardFind the surface area generated by revolving about the x-axis the curve y=2(15-x)^1/2, from x=0.59 to x=12.52arrow_forwardCarefully derive a formula for the length of a curve y = f(x) between x = a and x = b. Using this result, derive a formula for the surface area of a solid formed by rotating this curve around the x-axis. Your derivations should include clear diagrams where appropriate.arrow_forward
- (a) Set up an integral for the area of the surface obtained byrotating the curve about (i) thex x -axis and (ii) the y -axis.(b) Use the numerical integration capability of your calculatorto evaluate the surface areas correct to four decimal places. y =tan x , 0 ≤ x ≤ π/3arrow_forwardFind Area of a Surface of Revolution. Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the y-axis. y=1-(x2/4), 0≤x≤2arrow_forwardx^2+y^2=4 The part of the circle in the first region is rotated around the line x + y = 2. Calculate the area of the revolving surface that occurs.arrow_forward
- Find the surface area of revolution about the yy-axis of y=3√x over the interval 0≤x≤8. Enter your answer in terms of ππ or round to 4 decimal places.arrow_forwardFind the area of the surface given by z = f(x,y) over the region R. R: The triangle with vertices (0,0), (2,0), and (0,2) f(x,y) = 2x + 2y Answer: 6 (but how do I get there?)arrow_forward(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis. (b) Use the numerical integration capability of your calculator to evaluate the surface areas correct to four decimal places.arrow_forward
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