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How to integrate by using imaginary and real part of $e^{ix}$
I want to calculate integrals with $\sin(x)$ and $\cos(x)$ by real and imaginary part of $e^{ix}$. Assume $e^{ix}=\cos(x)+i\sin(x)$ For example $$ \begin{...
Apr 18, 2026
Archive: News
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Come up with some fun "equation Limericks"
We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks". A Limerick is a poem with five lines. The fir...
Apr 18, 2026
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How many different ways are there to choose 5 items from 12 distinct items if…
How many different ways are there to choose 5 items from 12 distinct items if… a. (5 pt.) the order of the items matters and repetition of items is not al...
Apr 18, 2026
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Linear transformation reflected across y-axis?
We have that: The linear transformation matrix for a reflection across the line $y = mx$ is: $$\frac{1}{1 + m^2}\begin{pmatrix}1-m^2&2m\\2m&m^2-1\...
Apr 18, 2026
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User Veridian Dynamics - Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Apr 18, 2026
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Checking linear dependence of two vectors in $\mathbb{R}^4$?
If we're given a set two vectors from $\mathbb{R}^4$, for example: $$S=\{(3,-1,1,1),(1,3,-1,1)\}$$ and we want to check if they're linearly depe...
Apr 18, 2026
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Pre-calculus Rug Area to room area problem.
A rectangular rug is in the middle of a room and there is a uniform width of floor that shows around the rug. The dimensions of the rug are 16ft by 21ft. ...
Apr 18, 2026
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User Ekesh Kumar - Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Apr 18, 2026
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tangent line vs secant line
According to definition, secant lines intersect the curve on two different points say $P,Q$ while tangent lines intersect only at one point. Also accordin...
Apr 18, 2026
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How can you prove that the square root of two is irrational?
I have read a few proofs that $\sqrt{2}$ is irrational. I have never, however, been able to really grasp what they were talking about. Is there a simplifi...
Apr 18, 2026
