What is the integral from 0 to 1 of sin(x^2) ?

The integral from 0 to 1 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*1)-sqrt(pi/2)\S(sqrt(2/pi)*0)

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integral from 0 to 1 of sin(x^2)

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

\frac{π}{2} § (\frac{2}{π} \cdot 1) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{1} 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)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 1) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} \cdot 1) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int 3 e^{7 x} d x

y^{^{'}} = x^{2} + 2 y

\int \frac{1 - tanh ^{3} ( 3 x )}{tanh ( 3 x )} d x

\int \frac{4 x ^{3}}{3} d x

0.5 y^{^{''}} + 10 y^{^{'}} + 100 y = 150

What is the integral from 0 to 1 of sin(x^2) ?
The integral from 0 to 1 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*1)-sqrt(pi/2)\S(sqrt(2/pi)*0)