Figure

EXAMPLE 5Finding a Definite Integral Using Technology

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

(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 $2.3918.$