Question

Use three trapezoids of equal width to approximate the integral of lnx between 1 and 4.

(1/2) + ln 12
ln 24
ln 12
(1/2) ln 24

Answer 1

\[\int_1^4\ln x~dx\approx\frac{1}{2}(0+\ln 2)+\frac{1}{2}(\ln 2+\ln 3)+\frac{1}{2}(\ln3+\ln4)\]
Simplify the right side and you're done.
(The height of each trapezoid is implied, since it's just 1.)

Answer 2

ln12?

Answer 3

\[\frac{1}{2}\ln 2+\frac{1}{2}\ln 2+\frac{1}{2}\ln 3+\frac{1}{2}\ln 3+\frac{1}{2}\ln 4\\
\ln 2+\ln 3+\frac{1}{2}\ln 2^2\\
\ln 2+\ln 3+\ln 2\\
2\ln 2+\ln 3\\
\ln 2^2+\ln 3\\
\ln 4+\ln 3\\
\ln12\]
Yup, that's right