University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

367

Pages:

4
Author:

Maria

QI y Qis the region bounded by the graph of u(y) the y-axis, y=0, and y= 6. Find the volume of the solid of revolution formed by revolving around the ar-axis Submit an exact answer in terms of 6 (2yf(y) dy = fary () dy = 2 dy 8 2.1%(6) - 8 y 32 Q2. R is the region bounded above by the graph of f(x)=zz and below by the z-axis over the interval [0, 1]. Find the volume of the solid of revolution formed by revolving R around the y-axis Submit an exact answer in terms of . x-x²-0 $ 2m x f(x)dx = 2(x)(x-x)dx 0 x(1-x)=0 =[(1)²-(1)"]= 6 Q3: R is the region bounded above by the graph of f(x)=2sin (222) +2 and below by the az axis over the interval 0, Find the volume of the solid of revolution formed by revolving R around the g-axis. Submit an exact answer in terms of 3 S 2 2x (2sin (2x)+2)dx = 2 (x2sin (2x2) +2x) olx 0 = 2 x 2 sin (2x)dx + 2 2x dx 4= 2x² - du= 4x dx 3 2. sin (u) du + 2 2 0 0 (-cos (u)) 0 (-cos (3)) - (-cos (0))] + 372 04: R is the region bounded above by the graph of f(z) = 6e and below by the az axis over the interval (0,2). Find the volume of the solid of revolution formed by revolving R around the y-axis. Submit an exact answer in terms of π. Step 3. The area of a cylindrical shell the circumference of a circle with radius ze the horizontal distance from the vertical zoos of rotationy times the height of the cylinder, given by the value of f(2). A(z)2nefie) ) =12se Step 4. We can atitain the volume of the solid by integrating the above area of a cylindrical shell over the interval (0,2). V(z) = A(z)da = 2xzf(z) de 12 Q5: R is the region bounded above by the graph of f(z) = 21 and below volume of the solid of revolution formed by revolving R around the y-axis. 10,3 by the a-axis over the interval 0, 3. Find the Submit an exact answer in terms of 0 2, 512 2x (221) d x = 2 x d x = 27.2.7x13 dx 3 0 = 3(33) Q6: R is the region bounded above by the graph of f(x)=72-72² and below by the az axis, Find the volume of the solid of revolution formed by revolving R around the line = 2. Submit an exact answer in terms of 7x-7x²=0 2 52 (2-x) (7x-7x²) dx 7x(1-x)=0 1 x=0x=1=2″) (14x-21x²+7x²³)dx