Chapter 7.8, Problem 47E

(a) If g(x) = (sin²x)/x², use your calculator or computer to make a table of approximate values of ${\displaystyle {\int }_1^{t}g\left(x\right)}dx$ for t = 2, 5, 10, 100, 1000, and 10,000. Does it appear that ${\displaystyle {\int }_1^{\infty }g\left(x\right)}dx$ is convergent?

(b) Use the Comparison Theorem with f(x) = 1/x² to show that ${\displaystyle {\int }_1^{\infty }g\left(x\right)}dx$ is convergent.

(c)     Illustrate part (b) by graphing f and g on the same screen for 1 „ x „ 10. Use your graph to explain intuitively why ${\displaystyle {\int }_1^{\infty }g\left(x\right)}dx$ is convergent.