Integral of Sinxcosy dy

The solution

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 oo                 
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 |  sin(x)*cos(y) dy
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-oo

$$\int\limits_{-\infty}^{\infty} \sin{\left(x \right)} \cos{\left(y \right)}\, dy$$

Integral(sin(x)*cos(y), (y, -oo, oo))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \sin{\left(x \right)} \cos{\left(y \right)}\, dy = \sin{\left(x \right)} \int \cos{\left(y \right)}\, dy$
1. The integral of cosine is sine:
  
  $\int \cos{\left(y \right)}\, dy = \sin{\left(y \right)}$
So, the result is: $\sin{\left(x \right)} \sin{\left(y \right)}$
Add the constant of integration:

$\sin{\left(x \right)} \sin{\left(y \right)}+ \mathrm{constant}$

The answer is:

$\sin{\left(x \right)} \sin{\left(y \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | sin(x)*cos(y) dy = C + sin(x)*sin(y)
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$$\int \sin{\left(x \right)} \cos{\left(y \right)}\, dy = C + \sin{\left(x \right)} \sin{\left(y \right)}$$

Simplify

The answer [src]

$$0$$

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

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Identical expressions

Integral of Sinxcosy dy

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The solution