What is the integral from 0 to 0.5 of ((sin(3x))/x) ?

The integral from 0 to 0.5 of ((sin(3x))/x) is \Si(1.5)

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integral from 0 to 0.5 of ((sin(3x))/x)

\int_{0}^{0.5} (\frac{sin ( 3 x )}{x}) d x

Si (1.5)

Solution steps

\int_{0}^{0.5} \frac{sin ( 3 x )}{x} d x

Apply u-substitution

: \int_{0}^{1.5} \frac{sin ( u )}{u} d u

= \int_{0}^{1.5} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= [Si (u)]_{0}^{1.5}

Compute the boundaries:

Si (1.5)

= Si (1.5)

\int_{2}^{4} \frac{3}{2 x + 1} d x

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\int_{- 2}^{0} 8 x + 2 x^{2} - x^{3} d x

\int_{0}^{6} x^{2} - 4 x d x

\int_{0}^{π} 2 cos (x) sin (x) d x

What is the integral from 0 to 0.5 of ((sin(3x))/x) ?
The integral from 0 to 0.5 of ((sin(3x))/x) is \Si(1.5)