Кратный интеграл

[CrypticMath]

Are these correct? (Являются ли эти правильно?)

a. Set up the double integral to find the volume bounded by $z = 2 + x$, $z = 0$, $x =0$, $y = 0$ and $y =1$.

$\displaystyle \int_0^2 \int_0^1 (2+x)\ dy\ dx$

b. Use double integrals, polar coordinates, to find the volume of the region above $z=0$, below $z=x$, between $y=\sqrt{4-x^2$ and $y=|x|$.

$\displaystyle \int_0^{\pi} \int_0^2 \sqrt{4-4sin^2 t}\ 2 cost\ dt\ d\theta$

c. Set up the triple integral in spherical coordinates to find the volume for $f(x,y,z) = e^{\left(x^2+y^2+z^2\right)^\frac32}$ on the region bounded by $z=\sqrt{4-x^2-y^2}$ and $z=0$.

$\displaystyle \int_0^\pi \int_0^{2\pi} \int_0^1 e^{(\rho)^2}^{\frac32} \rho^2 sin \phi\ d\rho\ d\theta\ d\phi$

[svv]

a. Нет.