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Solving integrals/ cosx*cosy

Integral of cosx*cosy dy

Limits of integration:

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The solution

You have entered [src] 
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∫0π2cos⁡(x)cos⁡(y) dy\int\limits_{0}^{\frac{\pi}{2}} \cos{\left(x \right)} \cos{\left(y \right)}\, dy 
Integral(cos(x)*cos(y), (y, 0, pi/2))
Detail solution

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

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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 | cos(x)*cos(y) dy = C + cos(x)*sin(y)
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∫cos⁡(x)cos⁡(y) dy=C+sin⁡(y)cos⁡(x)\int \cos{\left(x \right)} \cos{\left(y \right)}\, dy = C + \sin{\left(y \right)} \cos{\left(x \right)}
Simplify
The answer [src] 
cos(x)
cos⁡(x)\cos{\left(x \right)} 
=
= 
cos(x)
cos⁡(x)\cos{\left(x \right)} 
cos(x)

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

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