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

The integral from 0 to 1 of sin(y^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(y^2)

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

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

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} § (\frac{2}{π} y)]_{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_{0}^{π} 2 x cos (n x) d x

\int_{0}^{9} 2 x d x

\int_{0}^{4} (6 x^{3} - 3 x) d x

\int_{1}^{2} 5^{4 x} d x

\int_{5}^{9} \frac{1}{x - 4} d x

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