What is the integral from x to y of cos(t^2) ?

The integral from x to y of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)y)-sqrt(pi/2)\C(sqrt(2/pi)x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to y of cos(t^2)

\int_{x}^{y} cos (t^{2}) d t

\frac{π}{2} C (\frac{2}{π} y) - \frac{π}{2} C (\frac{2}{π} x)

Solution steps

\int_{x}^{y} cos (t^{2}) d t

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= [\frac{π}{2} C (\frac{2}{π} t)]_{x}^{y}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} y) - \frac{π}{2} C (\frac{2}{π} x)

= \frac{π}{2} C (\frac{2}{π} y) - \frac{π}{2} C (\frac{2}{π} x)

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

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

\int_{0}^{1} sin^{2} (\frac{π}{6} x) d x

\int_{7}^{9} arctan (\frac{7}{x}) d x

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

What is the integral from x to y of cos(t^2) ?
The integral from x to y of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)y)-sqrt(pi/2)\C(sqrt(2/pi)x)