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Solving integrals/ Sinxcosy

Integral of Sinxcosy dy

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  sin(x)*cos(y) dy
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∫−∞∞sin⁡(x)cos⁡(y) dy\int\limits_{-\infty}^{\infty} \sin{\left(x \right)} \cos{\left(y \right)}\, dy 
Integral(sin(x)*cos(y), (y, -oo, oo))
Detail solution

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

    ∫sin⁡(x)cos⁡(y) dy=sin⁡(x)∫cos⁡(y) dy\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:

      ∫cos⁡(y) dy=sin⁡(y)\int \cos{\left(y \right)}\, dy = \sin{\left(y \right)}

    So, the result is: sin⁡(x)sin⁡(y)\sin{\left(x \right)} \sin{\left(y \right)}

  2. Add the constant of integration:

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

The answer is:

sin⁡(x)sin⁡(y)+constant\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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∫sin⁡(x)cos⁡(y) dy=C+sin⁡(x)sin⁡(y)\int \sin{\left(x \right)} \cos{\left(y \right)}\, dy = C + \sin{\left(x \right)} \sin{\left(y \right)}
Simplify
The answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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