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How to use it?
- Integral of d{x}:
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Integral of (1-x^2)/(1+x^2)
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Integral of x*dx/(x^2+1)
- Integral of x^2*a^x
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Integral of sin^2*x
- cos(x^2+y^2)
- The double integral of:
- cos(x^2+y^2)
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Identical expressions
- cos(x^ two +y^ two)
- co sinus of e of (x squared plus y squared )
- co sinus of e of (x to the power of two plus y to the power of two)
- cos(x2+y2)
- cosx2+y2
- cos(x²+y²)
- cos(x to the power of 2+y to the power of 2)
- cosx^2+y^2
- cos(x^2+y^2)dx
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Similar expressions
- cos(x^2-y^2)
Integral of cos(x^2+y^2) dx
The solution
You have entered
[src]
1 / | | / 2 2\ | cos\x + y / dx | / 0
$$\int\limits_{0}^{1} \cos{\left(x^{2} + y^{2} \right)}\, dx$$
Integral(cos(x^2 + y^2), (x, 0, 1))
Detail solution
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Add the constant of integration:
FresnelCRule(a=1, b=0, c=y**2, context=cos(x**2 + y**2), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ / ___\ / ___\ \
___ ____ | / 2\ |x*\/ 2 | |x*\/ 2 | / 2\|
/ \/ 2 *\/ pi *|cos\y /*C|-------| - S|-------|*sin\y /|
| | | ____| | ____| |
| / 2 2\ \ \ \/ pi / \ \/ pi / /
| cos\x + y / dx = C + ------------------------------------------------------
| 2
/
$$\int \cos{\left(x^{2} + y^{2} \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(y^{2} \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}$$
The answer
[src]
/ / ___ \ / ___ \ \
___ ____ | / 2\ |\/ 2 | |\/ 2 | / 2\|
\/ 2 *\/ pi *|cos\y /*C|------| - S|------|*sin\y /|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
----------------------------------------------------
2
$$\frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(y^{2} \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$
=
=
/ / ___ \ / ___ \ \
___ ____ | / 2\ |\/ 2 | |\/ 2 | / 2\|
\/ 2 *\/ pi *|cos\y /*C|------| - S|------|*sin\y /|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
----------------------------------------------------
2
$$\frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(y^{2} \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(y^{2} \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$
sqrt(2)*sqrt(pi)*(cos(y^2)*fresnelc(sqrt(2)/sqrt(pi)) - fresnels(sqrt(2)/sqrt(pi))*sin(y^2))/2
Use the examples entering the upper and lower limits of integration.