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

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

\int_{x}^{x^{2}} sin (t^{2}) d t

\frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} x)

Solution steps

\int_{x}^{x^{2}} sin (t^{2}) d t

Use the nonelementary integral:

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

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

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} x)

= \frac{π}{2} § (\frac{2}{π} x^{2}) - \frac{π}{2} § (\frac{2}{π} x)

\int_{0}^{7} (7 x - x^{2}) d x

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

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

\int_{0}^{3} \frac{1}{x - 3} d x

\int_{0}^{1} 5 x^{4} d x

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