Daily math problems for May 25, 2026 — Analytic Geometry, Calculus, Trigonometric identities

Slope $=2$. The line through $(0,1)$: $y-1=2(x-0)\Rightarrow y=2x+1$.

$u=x$, $du=dx$, $v=\sin x$. $\int x\cos xdx=x\sin x-\int \sin xdx=x\sin x+\cos x+C$.

The fifth roots of unity sum to $0$. Subtracting the root $1$ leaves a sum of $-1$, and taking real parts gives $\cos \frac{2\pi }{5}+\cos \frac{4\pi }{5}+\cos \frac{6\pi }{5}+\cos \frac{8\pi }{5}=-1$.