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Solving integrals/ cos(x+y)

Integral of cos(x+y) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01cos⁡(x+y) dx\int\limits_{0}^{1} \cos{\left(x + y \right)}\, dx 
Integral(cos(x + y), (x, 0, 1))
Detail solution

  1. Let u=x+yu = x + y.

    Then let du=dxdu = dx and substitute dudu:

    ∫cos⁡(u) du\int \cos{\left(u \right)}\, du

    1. The integral of cosine is sine:

      ∫cos⁡(u) du=sin⁡(u)\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}

    Now substitute uu back in:

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

  2. Add the constant of integration:

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

The answer is:

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

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

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

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