JEE Advanced 2025 · Paper 2, Mathematics question 2

Corners.

• The lines $y=\frac{5x-1}{4}$ and $y=\frac{17}{4}-x$ meet at $(2,\frac94)$.
• $y=\frac1x$ meets the first line at $x=1$.
• $y=\frac1x$ meets the second line at $x=4$.

Area.
$$\int_1^2\left(\frac{5x-1}{4}-\frac1x\right)dx+\int_2^4\left(\frac{17}{4}-x-\frac1x\right)dx.$$
The first integral is $\frac{13}{8}-\ln2$ and the second is $\frac52-\ln2$, so
$$\text{Area}=\frac{13}{8}+\frac52-2\ln2=\frac{33}{8}-\log_e4.$$