query: Find the volume bounded by the $xy$ plane, cylinder $x^2 + y^2 = 1$ and sphere $x^2 + y^2 +z^2 = 4$
positive_passages.docid: 142495
positive_passages.text: Find the volume of the region inside both the sphere $x^2+y^2+z^2=4$ and the cylinder $x^2+y^2=1$
negative_passages.docid: 78719
negative_passages.text: Solve the DE $yy^{\prime}+x=\sqrt{x^2+y^2}$
negative_passages.docid: 125907
negative_passages.text: Why does the integral of the surface area of a sphere equal its volume?
negative_passages.docid: 56433
negative_passages.text: Volume form on $(n-1)$-sphere $S^{n-1}$
negative_passages.docid: 104227
negative_passages.text: How to obtain the limit of $xy\log(x^2+y^2)$ when $(x,y)\to(0,0)$ without using polar coordinates or L'Hôpital?
negative_passages.docid: 27911
negative_passages.text: How can I prove that $xy\leq x^2+y^2$?
negative_passages.docid: 39015
negative_passages.text: Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
negative_passages.docid: 52103
negative_passages.text: Use Stokes's Theorem to show $\oint_{C} y ~dx + z ~dy + x ~dz = \sqrt{3} \pi a^2$
negative_passages.docid: 15586
negative_passages.text: Volume of the torus with an integral
negative_passages.docid: 80157
negative_passages.text: Parametrization for intersection of sphere and plane. $x^2+y^2+z^2=81$, $x+y+z=15$.
negative_passages.docid: 61105
negative_passages.text: solve$\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}$
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$
negative_passages.docid: 34428
negative_passages.text: Find equation of a plane throw two given point and orthogonal to another space
negative_passages.docid: 134569
negative_passages.text: How to sum 2 vectors in spherical coordinate system
negative_passages.docid: 138060
negative_passages.text: Using NSolve in the complex plane
negative_passages.docid: 85917
negative_passages.text: Solve $(x+1)^y-x^z=1$
negative_passages.docid: 41550
negative_passages.text: Find the Area of the ellipse