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Solving integrals/ cos(x)cos(y)

Integral of cos(x)cos(y) dx

Limits of integration:

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The solution

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∫01cos⁡(x)cos⁡(y) dx\int\limits_{0}^{1} \cos{\left(x \right)} \cos{\left(y \right)}\, dx 
Integral(cos(x)*cos(y), (x, 0, 1))
Detail solution

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

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

    1. The integral of cosine is sine:

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

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫cos⁡(x)cos⁡(y) dx=C+sin⁡(x)cos⁡(y)\int \cos{\left(x \right)} \cos{\left(y \right)}\, dx = C + \sin{\left(x \right)} \cos{\left(y \right)}
Simplify
The answer [src] 
cos(y)*sin(1)
sin⁡(1)cos⁡(y)\sin{\left(1 \right)} \cos{\left(y \right)} 
=
= 
cos(y)*sin(1)
sin⁡(1)cos⁡(y)\sin{\left(1 \right)} \cos{\left(y \right)} 
cos(y)*sin(1)

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

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