Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Find the volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis

Sagot :

shubhamchouhanvrVT

The volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be  

V = 8π/3

What is volume integration?

When the integration is done in the three dimensions in the three coordinates x,y and z then we will call it as a volume integration.

I set y=2x = y=2 to find where the intersect each others so I can have my boundaries for integration.

You goal is to find the area so you can integrate around that area. We're revolving around the x-axis so the area will be a circle.

V = ∫A(x)dx =  ∫(πr²)dr

Since we have two different radius, we subtract them from each others.

∫(πr₂² - πr₁²)dr

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Hence the volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be V = 8π/3

To know more about Volume integration follow

https://brainly.com/question/18371476

#SPJ4

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.