At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
The value of the expression on evaluation is 96π / 5.
Here we have to find the value of the expression.
∫∫∫x² dV
E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.
E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].
∫∫∫ x² dV = ∫[tex]\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0[/tex] r² cos² Фrd dФ
= [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,[/tex]r³ cos²Ф dz dr dФ
= [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,[/tex] 3[tex]r^{4}[/tex]cos²Ф dr dФ
= 3 [tex]\int\limits^2\pi _0 {} \,[/tex] 1/2 [tex]2^{5}[/tex]/ 5 ( 1 + cos² Ф )dr dФ
= 48 / 5 [( Ф + 1/2 sin 2Ф)[tex]]^{2\pi } _{0}[/tex]
= 96π / 5
Therefore the value of the expression is 96π/5.
To know more about the integration refer to the link given below:
https://brainly.com/question/27419605
#SPJ4
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
