A 3-D object is created by rotating the area between Ye) and the x-axis about the line y -1.5 fro...
1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) around: 1. the r-axis with y20 2. the y-axis with 20 You will need to clearly show how you have chosen to break the surface up into tiny pieces and what high school geometry is needed to find the area of these tiny pieces (b) (6 marks) Confirm that your formula provides the expected surface areas...
Compute the volume of the solid created by rotating the area between the graphs of y = ? and the y z2 between x = 0 and x = 1 around the x-axis.
4. [8 points] What is the volume of the solid formed by taking the the area between y = 4- 4x and the x-axis on the interval [0,1], and rotating it about x = 2? Fill in the following blanks to show your work and final answer. Setup but do not solve the definite integral. Volume of slice: Riemann Sum: Sketch of picture: Definite Integral:
2. Find the surface area of the object obtained s 2 about the y-axis. by rotating y: 478x2,15*
Compute the volume of the solid created by rotating the area bounded by the curve y= ex and the x-axis between 2 = O anda 1 around the y-axis. -
Compute the volume of the solid created by rotating the area bounded by the curve y=er and the x-axis between 2 = O and x = 1 around the y-axis.
Q14 Find the distance from x=3 to x = 8 on the graph of y als Find the area of the surface generated by rotating y = 25*56 about the y-axis. Bonus: (1) Draw the region that is represented by the following definite integral which represents the volume of a solid generated by rotating the region about some axis. Be sure to label the curves and the axis of revolution: 2 (2 - y)- y)dy
na 2 = ža Compute the volume of the solid created by rotating the area between the graph of y= sin(2) cos(x) and the x-axis between c = () and I = į around the x-axis.
Find the exact area of the surface obtained by rotating the curve about the x-axis. y 2x 2 6 1SXS를 플+을- 263 X\ 266 Find the exact area of the surface obtained by rotating the curve about the x-axis. y 2x 2 6 1SXS를 플+을- 263 X\ 266
Find the volume of the solid created by rotating y=x + 4 around the y-axis, O SX54. Give your answer as a decimal rounded to four decimal places.