What is the integral from 0 to pi/4 of sin(x^2) ?

The integral from 0 to pi/4 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi) pi/4)-sqrt(pi/2)\S(sqrt(2/pi)*0)

Popular >

integral from 0 to pi/4 of sin(x^2)

\int_{0}^{\frac{π}{4}} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{\frac{π}{4}} 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}^{\frac{π}{4}}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int_{- 6}^{6} 6^{2} - x^{2} d x

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

\int_{0}^{π} x sin^{3} (x) d x

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

\int_{0}^{1} (x^{2} + 5) e^{2 x} d x

What is the integral from 0 to pi/4 of sin(x^2) ?
The integral from 0 to pi/4 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi) pi/4)-sqrt(pi/2)\S(sqrt(2/pi)*0)