What is the integral from 2t to 3t of (sin(x))/(2x) ?

The integral from 2t to 3t of (sin(x))/(2x) is 1/2 (\Si(3t)-\Si(2t))

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integral from 2t to 3t of (sin(x))/(2x)

\int_{2 t}^{3 t} \frac{sin ( x )}{2 x} d x

\frac{1}{2} (Si (3 t) - Si (2 t))

Solution steps

\int_{2 t}^{3 t} \frac{sin ( x )}{2 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{2 t}^{3 t} \frac{sin ( x )}{x} d x

Use the nonelementary integral:

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

= \frac{1}{2} [Si (x)]_{2 t}^{3 t}

Compute the boundaries:

Si (3 t) - Si (2 t)

= \frac{1}{2} (Si (3 t) - Si (2 t))

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What is the integral from 2t to 3t of (sin(x))/(2x) ?
The integral from 2t to 3t of (sin(x))/(2x) is 1/2 (\Si(3t)-\Si(2t))