3.79: Integration identity and shaded area

Show that $\displaystyle\int\frac{1}{3x+4}\,\mathrm{d}x=\frac13\ln|3x+4|+c$.

The line $y=\dfrac{7-3x}{10}$ and curve $y=\dfrac{1}{3x+4}$ meet at $A$. Verify that the $y$-coordinate of $A$ is $0.1$ and calculate the shaded area.