Pregunta
Using the disc method, find the volume of the solid formed by revolving the region bounded by
and
from
to
about the x-axis.
Ask by Salazar West. in Portugal
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The volume of the solid is
.
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Como
Mind Expander
To find the volume of the solid formed by revolving the region bounded by
and
from
to
about the x-axis using the disk method, we start by determining the radius of the disks. The radius at any point
is given by the value of the function
.
The volume
can be calculated using the following integral formula:
In this case,
,
, and
. Thus, we can set up the integral:
This simplifies to:
Now we compute the integral:
Evaluating this from 0 to 2 gives:
Finally, we multiply by
:
Thus, the volume of the solid is:
So, the volume of the solid formed by revolving the region bounded by
and
from
to
about the x-axis is
cubic units.

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium