Sine-integral function The integral sin t dt, Si (x) = / 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 sin t dt. If it converges, what is its value?

Question
Sine-integral function
The integral
sin t
dt,
Si (x) = /
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
sin t
dt.
If it converges, what is its value?
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Transcribed Image Text

Sine-integral function The integral sin t dt, Si (x) = / 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 sin t dt. If it converges, what is its value?