Chapter 12: Q2RE (page 752)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
The given statement is False.
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Use symmetry to evaluate the double integral \(\iint\limits_R {\frac{{xy}}{{1 + {x^4}}}dA}\), \(R = \{ (x, y)| - 1 \le x \le 1,0 \le y \le 1\} \).
Under the cone \({\rm{z = }}\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} {\rm{ }}\)and above the disk\({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ }} \le {\rm{ 4}}\)
\(\int\limits_{ - 2}^2 {\int\limits_0^{\sqrt {4 - {y^2}} } {f(x,y)dy} dx} \)
Sketch the solid whose volume is given by the integrated integral
\(\int\limits_0^1 {\int\limits_0^1 {\left( {4 - x - 2y} \right)} } dxdy\)
Describe in words the surface whose equation is given
\({\rm{r = 5}}\).
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