Find the volume of the solid obtained by rotating the region enclosed by x=9y, y^3=x, yâ¥0 about the y-axis using the method of disks or washers.

2. Find the volume of the solid obtained by rotating the region bounded by y=1/4 (x^2), x=2 and y=0 about the y-axis. Below is a graph of the bounded region.

09db3956-4112-3e44-b7e8-f16172a0e38b_a

3. Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y=4+3xâx^2 and y+x=4 and y+x=4 about the y-axis. Below is a graph of the bounded region.

3805fe1a-31bc-3dce-92e3-04280ddcaf9e_7

4. Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of f(x)=x^2+2 for 0â¤ x â¤5 about the y-axis.
0b2d55a4-f496-3180-bc33-3ef52939c407___2

5. The volume of the solid obtained by rotating the region enclosed by x=0, y=1, x=y^4 about the line y=1 can be computed using the method of disks or washers via an integral. Find the volume in cubic units?

6. The volume of the solid obtained by rotating the region enclosed by

y=e^(2x)+1, y=0, x=0, x=0.6 about the x-axis can be computed using the method of disks or washers via an integral. Find the volume in cuibic units??

Question

contestada

Respuesta :

zubam2002 zubam2002 · Answer 1 · 2020-02-11T00:56:04+01:00

Answer:

Step-by-step explanation:

1) 9y - y³= 0

y(9 - y²) =0

y = 0 and y² - 9 = 0 ⇒ y² = 9 ⇒ y = √9 = ±3

V =∫↑b↓aπx²dy

V = ∫↑3↓oπ(9y - y³)²dy

V = π∫(81y² - 18y∧4 + y∧6)dy

V = π( 81y³/3 - 18y∧5/5 + y∧7/7)↑3↓0 = π(27y³ - 18y∧5/5 + y∧7/7)↑3↓0

2) x =2 and y = 1/4x²

From y = 1/4x² ⇒ 1/y = 4x² ⇒ x² = 1/4y ⇒ x = √1/4y ⇒ x = 1/2√y

When x = 2: y = 1/16

Answer Link