Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
The volume of a solid is [tex]\frac{26}{3} \pi[/tex].
Given
The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis
Curve is y = x + 1
Line is y = 0
We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.
If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.
Volume of a solid:
According to washer method:
[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]
Using washer method, where a=0 and b=2, we get
V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]
= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]
= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]
= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]
= [tex]\pi [\frac{26}{3}][/tex]
= [tex]\frac{26}{3} \pi[/tex]
Therefore the volume of a solid is [tex]\frac{26}{3} \pi[/tex].
Find out more information about volume of a solid here
https://brainly.com/question/12894092
#SPJ4
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
