Интеграл cos(y^2) (dx)

Вы ввели

  1           
  /           
 |            
 |     / 2\   
 |  cos\y / dy
 |            
/             
0             

$$\int_{0}^{1} \cos{\left (y^{2} \right )}\, dy$$

Ответ

                                      /  ___ \           
  1                ___   ____         |\/ 2  |           
  /              \/ 2 *\/ pi *fresnelc|------|*gamma(1/4)
 |                                    |  ____|           
 |     / 2\                           \\/ pi /           
 |  cos\y / dy = ----------------------------------------
 |                             8*gamma(5/4)              
/                                                        
0                                                        

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left( \sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2 }}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf} \left(\sqrt{-i}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\right)\right) }\over{16}}$$

Численный ответ

0.904524237900272

Ответ (Неопределённый)

                                         /    ___\           
                      ___   ____         |y*\/ 2 |           
  /                 \/ 2 *\/ pi *fresnelc|-------|*gamma(1/4)
 |                                       |   ____|           
 |    / 2\                               \ \/ pi /           
 | cos\y / dy = C + -----------------------------------------
 |                                 8*gamma(5/4)              
/                                                            

$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,y}\over{2}} \right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left({{ \left(\sqrt{2}\,i-\sqrt{2}\right)\,y}\over{2}}\right)+\left(-\sqrt{2 }\,i-\sqrt{2}\right)\,\mathrm{erf}\left(\sqrt{-i}\,y\right)+\left( \sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1 }\over{4}}}\,y\right)\right)}\over{16}}$$