Question

Evaluation of $~\iint_{D} {x^2-y^2 \over 1+x^4+y^4 } \mathrm{d}x \mathrm{d}y~$ where $~D~$is of bounded and closed and line symmetric with $~y=x$

score 116 · Answer 1 · 2026-03-26 08:13:52

116

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108

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60

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51

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List Question

Evaluation of $~\iint_{D} {x^2-y^2 \over 1+x^4+y^4 } \mathrm{d}x \mathrm{d}y~$ where $~D~$is of bounded and closed and line symmetric with $~y=x$

Find the domain to make the integral max

How to find the limit of $a_n=\int_{\mathcal{D}}(3xy-x^2y-xy^2)^n\lambda_2(dx dy)$ on $\mathcal{D}=\{(x,y)\in\mathbb{R}^2|x\gt0,y\gt0,x+y\lt3\}$

Flux through complex surface

Multiple integral involving exponential function

Converting the double integral in polar coordinates to Cartesian coordinates

Finding the area of the region cut from the first quadrant by the curve

Find the average distance from a point $P(x,y)$ in the disk.

Evaluating the integral $\int_0^1\int_0^1\frac{y}{1+xy}dxdy$

Multiple integral problem (limits interchanged)

volume of the region in the first octant bounded by the coordinate planes and the planes

Double integral objective question.

Multiple integral and area of a sphere

Solution Verification in change from rectangular to spherical coordinates of an improper triple integral.

Formula for certain path-ordered integrals

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