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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

\int_{0}^{y} 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}^{y}

Compute the boundaries:

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

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

\int_{0}^{l n (2)} e^{6 x} d x

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

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

\int_{4}^{9} 5 x d x

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

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