What is the integral from-1/2 to 1 of (sin(x^2))/x ?

The integral from-1/2 to 1 of (sin(x^2))/x is -0.5\Si(1/4)+0.4730415352

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integral from-1/2 to 1 of (sin(x^2))/x

\int_{- \frac{1}{2}}^{1} \frac{sin ( x ^{2} )}{x} d x

- 0.5 Si (\frac{1}{4}) + 0.4730415352

Solution steps

\int_{- \frac{1}{2}}^{1} \frac{sin ( x ^{2} )}{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_{- \frac{1}{2}}^{0} \frac{sin ( x ^{2} )}{x} d x + \int_{0}^{1} \frac{sin ( x ^{2} )}{x} d x

\int_{- \frac{1}{2}}^{0} \frac{sin ( x ^{2} )}{x} d x = - \frac{1}{2} Si (\frac{1}{4})

\int_{0}^{1} \frac{sin ( x ^{2} )}{x} d x = 0.4730415352

= - \frac{1}{2} Si (\frac{1}{4}) + 0.4730415352

Simplify

= - 0.5 Si (\frac{1}{4}) + 0.4730415352

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What is the integral from-1/2 to 1 of (sin(x^2))/x ?
The integral from-1/2 to 1 of (sin(x^2))/x is -0.5\Si(1/4)+0.4730415352