Sign convention flip

What goes wrong

Carries a sign convention chosen at the start into a term where the convention reverses.

Next time

Substitute negative values and directional terms inside explicit parentheses before simplifying, writing out forms like $y_2 - (y_1)$ to prevent carrying over an accidental positive sign.

Questions that set this trap

6 published questions

mathematicsThe value of the integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \left( \frac{4 - \operatorname{cosec}^2 x}{\cos^4 x} \right) dx$ is :
mathematicsLet $\mathrm{I}(\mathrm{x})=\int \frac{(\mathrm{x}+1)}{\mathrm{x}\left(1+\mathrm{xe}^{\mathrm{x}}\right)^{2}} \mathrm{dx}, \mathrm{x}>0$ , I…
mathematicsThe shortest distance between the lines $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is
mathematicsLet the plane $P : 4x - y + z = 10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane $x + y - z = 4$ . I…
mathematicsIf $\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous function satisfying…
mathematicsThe value of the integral $\int_{-\log_e 2}^{\log_e 2} e^x \left( \log_e \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx$ is equal to