Question

(a) Use a CAS to graph the solution curve of the initial-valueproblem in Problem $Si\left(x\right)=\underset{0}{\overset{x}{\int }}\frac{sint}{t}dt$on the interval $\left(0,\infty \right)$

(b) Use a CAS to find the value of the absolute maximum of the solution y(x)on the interval.

Short answer

$(1.688,1.742)$The highest possible value in the coordinates

Step-by-step solution

(a) Given Information.

The function is:

$Si\left(x\right)=\underset{0}{\overset{x}{\int }}\frac{sint}{t}dt$

Indicating value in graph

$y=10x^{-2}\left[Si\left(x\right)-Si\left(1\right)\right]$

(b) Appling CAS

We can observe from the graph in part (a) that the absolute maximum occurs around $x=1.7$. Using CAS, we can determine the root and then solve the constraint$y\text{'}\left(x\right)=0$. The greatest value is then discovered to be in the coordinates$(1.688,1.742)$

Result

The highest possible value in the coordinates$(1.688,1.742)$