Question

If \(\large\displaystyle\int_2^k \dfrac{1}{x+2} dx = \ln 2\), find the value of \(\large k\).

Answer 1

you have a definite integral that when solved with give you the difference of two logarithms which when solved using algebra will yield k

\[\left[ \ln \left| k + 2 \right| - \ln \left| 2 + 2 \right|\right] = \ln 2\]

Answer 2

combine the difference into a quotient than you can remove the logs and solve for k