What is the integral from-5 to 5 of (sin(x))/x ?

The integral from-5 to 5 of (sin(x))/x is -\Si(-5)+1.54993…

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integral from-5 to 5 of (sin(x))/x

\int_{- 5}^{5} \frac{sin ( x )}{x} d x

- Si (- 5) + 1.54993 \dots

Solution steps

\int_{- 5}^{5} \frac{sin ( x )}{x} d x

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 5}^{0} \frac{sin ( x )}{x} d x + \int_{0}^{5} \frac{sin ( x )}{x} d x

\int_{- 5}^{0} \frac{sin ( x )}{x} d x = - Si (- 5)

\int_{0}^{5} \frac{sin ( x )}{x} d x = 1.54993 \dots

= - Si (- 5) + 1.54993 \dots

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What is the integral from-5 to 5 of (sin(x))/x ?
The integral from-5 to 5 of (sin(x))/x is -\Si(-5)+1.54993…