Chapter 12: Q 6E (page 740)
Describe in words the surface whose equation is given\({\rm{\rho = 3}}\).
The surface of the given equation is the sphere of radius \({\rm{3}}\) centered at the origin.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Sketch the solid whose volume is given by the integrated integral.
\(\int\limits_0^1 {\int\limits_0^1 {\left( {2 - {x^2} - {y^2}} \right)dydx} } \)
The average value of a function \(f\left( {x,y} \right)\) over a rectangle \(R\) is defined to be .
Find the average value of \(f\) over the given rectangle, \(f\left( {x,y} \right) = {e^y}\sqrt {x + {e^y}} \), \(R = \left( {0,4} \right) \times \left( {0,1} \right)\).
Evaluate the double integral:\begin{gathered}\iint\limits_D {{x^3}dA,} \hfill \\D = \{ x,y)/1 \leqslant x \leqslant e,0 \leqslant y \leqslant lnx\} \hfill \\\end{gathered}
Evaluate the double integral:\(\iint\limits_D {xdA,D = \{ (x,y)/0 \leqslant x \leqslant \Pi ,0 \leqslant y \leqslant sinx\} }\)
Write the equations in cylindrical coordinates.
a. \({\rm{3x + 2y + z = 6}}\)
b. \({\rm{ - }}{{\rm{x}}^{\rm{2}}}{\rm{ - }}{{\rm{y}}^{\rm{2}}}{\rm{ + }}{{\rm{z}}^{^{\rm{2}}}}{\rm{ = 1}}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
