Finding a Definite Integral Using Technology

1. Use a graphing utility to find \(\int_{1/2}^{4}\ln x\,dx\)
2. Use a computer algebra system to find \(\int_{1/2}^{4}\ln x\,dx.\)

Solution (a) A graphing utility, such as a TI-84, provides only an approximate numerical answer to the integral \(\int_{1/2}^{4}\ln x\,dx.\) As shown in Figure 21, \(\int_{1/2}^{4}\ln\, x\,dx\approx 2.391751035\).

(b) Because a computer algebra system manipulates symbolically, it can find an exact value of the definite integral. Using MuPAD in Scientific WorkPlace, we get \[ \int_{1/2}^{4}\ln x\,dx= \dfrac{17}{2}\ln 2-\dfrac{7}{2} \]

An approximate numerical value of the definite integral using MuPAD is \(2.3918.\)