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

The integral from a to b of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)b)-sqrt(pi/2)\S(sqrt(2/pi)a)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from a to b of sin(x^2)

\int_{a}^{b} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} b) - \frac{π}{2} § (\frac{2}{π} a)

Solution steps

\int_{a}^{b} 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)]_{a}^{b}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} b) - \frac{π}{2} § (\frac{2}{π} a)

= \frac{π}{2} § (\frac{2}{π} b) - \frac{π}{2} § (\frac{2}{π} a)

\int_{0}^{a} x e^{- x} d x

\int_{0}^{l n (A)} 6 e^{3 x} d x

\int_{c o s (x)}^{1} 1 - x^{2} d x

\int_{1}^{6} (\frac{1}{x}) d x

\int_{0}^{1} \frac{1}{5 x} d x

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