Recently published items

3 Forces Applied to an Eye bolt.  Use force components to calculate the Reaction force.

set of exercises on double and triple integrals

moment of inertia - cylinder

Double integral in polar coordinates - concentric circles

mass of tetrahedron via integration

Volume of a tetrahedron using integrals

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Inputing Integrals tutorial

3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.