What is the integral from-x to x of cos(t^2+1) ?

The integral from-x to x of cos(t^2+1) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-x to x of cos(t^2+1)

\int_{- x}^{x} cos (t^{2} + 1) d t

cos (1) (\frac{π}{2} C (\frac{2}{π} x) - \frac{π}{2} C (- \frac{2}{π} x)) - sin (1) (\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (- \frac{2}{π} x))

Solution steps

\int_{- x}^{x} cos (t^{2} + 1) d t

Rewrite using trig identities

= \int_{- x}^{x} cos (t^{2}) cos (1) - sin (t^{2}) sin (1) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- x}^{x} cos (t^{2}) cos (1) d t - \int_{- x}^{x} sin (t^{2}) sin (1) d t

\int_{- x}^{x} cos (t^{2}) cos (1) d t = cos (1) (\frac{π}{2} C (\frac{2}{π} x) - \frac{π}{2} C (- \frac{2}{π} x))

\int_{- x}^{x} sin (t^{2}) sin (1) d t = sin (1) (\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (- \frac{2}{π} x))

= cos (1) (\frac{π}{2} C (\frac{2}{π} x) - \frac{π}{2} C (- \frac{2}{π} x)) - sin (1) (\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (- \frac{2}{π} x))

What is the integral from-x to x of cos(t^2+1) ?
The integral from-x to x of cos(t^2+1) is