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

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

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

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

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} § (\frac{2}{π} x)]_{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_{2}^{5} 7 - 3 x d x

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

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

\int_{4}^{4} 1

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

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