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

The integral from 1 to x of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)x)-sqrt(pi/2)\S(sqrt(2/pi)*1)

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integral from 1 to x of sin(t^2)

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

\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

Solution steps

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

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= [\frac{π}{2} § (\frac{2}{π} t)]_{1}^{x}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

= \frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

\int_{0}^{1} x^{2} e^{- x^{3}} d x

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{3}} d x

\int_{0}^{3} x e^{2 x} d x

\int_{0}^{4} \frac{1}{( x - 3 ) ^{2}} d x

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

What is the integral from 1 to x of sin(t^2) ?
The integral from 1 to x of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)x)-sqrt(pi/2)\S(sqrt(2/pi)*1)