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Solving integrals/ sin(x^2+y^2)

Integral of sin(x^2+y^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
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 |     / 2    2\   
 |  sin\x  + y / dx
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0
$$\int\limits_{0}^{1} \sin{\left(x^{2} + y^{2} \right)}\, dx$$ 
Integral(sin(x^2 + y^2), (x, 0, 1))
Detail solution

    FresnelSRule(a=1, b=0, c=y**2, context=sin(x**2 + y**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                                      /         /    ___\    /    ___\        \
                           ___   ____ |   / 2\  |x*\/ 2 |    |x*\/ 2 |    / 2\|
  /                      \/ 2 *\/ pi *|cos\y /*S|-------| + C|-------|*sin\y /|
 |                                    |         |   ____|    |   ____|        |
 |    / 2    2\                       \         \ \/ pi /    \ \/ pi /        /
 | sin\x  + y / dx = C + ------------------------------------------------------
 |                                                 2                           
/
$$\int \sin{\left(x^{2} + y^{2} \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(y^{2} \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}$$
Simplify
The answer [src] 
             /         /  ___ \    /  ___ \        \
  ___   ____ |   / 2\  |\/ 2  |    |\/ 2  |    / 2\|
\/ 2 *\/ pi *|cos\y /*S|------| + C|------|*sin\y /|
             |         |  ____|    |  ____|        |
             \         \\/ pi /    \\/ pi /        /
----------------------------------------------------
                         2
$$\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(y^{2} \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$ 
=
= 
             /         /  ___ \    /  ___ \        \
  ___   ____ |   / 2\  |\/ 2  |    |\/ 2  |    / 2\|
\/ 2 *\/ pi *|cos\y /*S|------| + C|------|*sin\y /|
             |         |  ____|    |  ____|        |
             \         \\/ pi /    \\/ pi /        /
----------------------------------------------------
                         2
$$\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(y^{2} \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$ 
sqrt(2)*sqrt(pi)*(cos(y^2)*fresnels(sqrt(2)/sqrt(pi)) + fresnelc(sqrt(2)/sqrt(pi))*sin(y^2))/2

    Use the examples entering the upper and lower limits of integration.

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