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

The integral from 2 to x^2 of (sin(t))/t is \Si(x^2)-1.60541…

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

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

Si (x^{2}) - 1.60541 \dots

Solution steps

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

Use the nonelementary integral:

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

= [Si (t)]_{2}^{x^{2}}

Compute the boundaries:

Si (x^{2}) - 1.60541 \dots

= Si (x^{2}) - 1.60541 \dots

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

\int_{0}^{\frac{1}{2}} \frac{x}{2 + 32 x ^{4}} d x

\int_{0}^{4} 2 x + 3 d x

\int_{0}^{\frac{8}{5}} \frac{1}{25 x ^{2} + 64} d x

\int_{1}^{e} 10 x ln (x) d x

What is the integral from 2 to x^2 of (sin(t))/t ?
The integral from 2 to x^2 of (sin(t))/t is \Si(x^2)-1.60541…