sophiqdionacles5644 sophiqdionacles5644
  • 15-03-2024
  • Mathematics
contestada

Consider the region bounded by the surfaces z = x and z = x², and the planes y = 0 and y = 5. Write an integral to find the volume of the region.

Respuesta :

nikvist
nikvist nikvist
  • 15-03-2024

Answer:

Step-by-step explanation:

[tex]z=x,\quad z=x^2,\quad 0\leq y\leq 5\\x=x^2,\quad x-x^2=0,\quad x(1-x)=0,\quad x=0\vee x=1\\V=\int_0^1 (x-x^2)dx\cdot\int_0^5dy=\left.\left(\frac{x^2}{2}-\frac{x^3}{3}\right)\right|_0^1\cdot 5=\left(\frac{1}{2}-\frac{1}{3}\right)\cdot 5=\frac{5}{6}[/tex]

Answer Link

Otras preguntas

Why does Romeo call himself “fortune’s fool”?
The edge length of a cube-shaped box is 2√5 inches long. Estimate the length of the edge to the nearest tenth of an inch. Then explain why you can only estimate
Write about what consequences, both positive and negative, Hamlet's "antic disposition" may have in the play.
if the expression below has a positive value , which inequality represents all possible values of x in the expression? -3x
Read the excerpt from The evolution of useful things
Write an expression in simplest form for the area of this shape.
Use the adjusted trial balance for stockton company below to answer the questions that follow. stockton company adjusted trial balance december 31 cash 6,530 ac
In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=17°, and RS = 84 feet. Find the length of QR to the nearest tenth of a foot.​
What is the measure of the missing angle?!
Your firm is a supplier to a major chain of discount stores. you have heard rumors that this chain of discount stores is in financial difficulty. which financia