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Theory and ExamplesSine-integral function The integral
Chapter 8, Problem 77E(choose chapter or problem)
Problem 77E
Theory and Examples
Sine-integral function The integral
called the sine-integral function, has important applications in optics.
a. Plot the integrand (sin t)/t for t > 0 Is the sine-integral function everywhere increasing or decreasing? Do you think Si (x) = 0 for x > 0? Check your answers by graphing the function Si (x) for 0 ≤ x ≤25.
b. Explore the convergence of
If it converges, what is its value?
Questions & Answers
QUESTION:
Problem 77E
Theory and Examples
Sine-integral function The integral
called the sine-integral function, has important applications in optics.
a. Plot the integrand (sin t)/t for t > 0 Is the sine-integral function everywhere increasing or decreasing? Do you think Si (x) = 0 for x > 0? Check your answers by graphing the function Si (x) for 0 ≤ x ≤25.
b. Explore the convergence of
If it converges, what is its value?
ANSWER:
SOLUTION:
Step 1 of 4:
In this question, (a) Plot the integrand for . State the sine-integral function everywhere increasing or decreasing. Check for . Check the answers by graphing the function for . (b). Explore the convergence of
If it converges, find is its value.