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Solving integrals/ sqrt(2)*cos(x)

Integral of sqrt(2)*cos(x) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  m                
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∫0m2cos⁡(x) dx\int\limits_{0}^{m} \sqrt{2} \cos{\left(x \right)}\, dx 
Integral(sqrt(2)*cos(x), (x, 0, m))
Detail solution

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

    ∫2cos⁡(x) dx=2∫cos⁡(x) dx\int \sqrt{2} \cos{\left(x \right)}\, dx = \sqrt{2} \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: 2sin⁡(x)\sqrt{2} \sin{\left(x \right)}

  2. Add the constant of integration:

    2sin⁡(x)+constant\sqrt{2} \sin{\left(x \right)}+ \mathrm{constant}

The answer is:

2sin⁡(x)+constant\sqrt{2} \sin{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
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 | \/ 2 *cos(x) dx = C + \/ 2 *sin(x)
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∫2cos⁡(x) dx=C+2sin⁡(x)\int \sqrt{2} \cos{\left(x \right)}\, dx = C + \sqrt{2} \sin{\left(x \right)}
Simplify
The answer [src] 
  ___       
\/ 2 *sin(m)
2sin⁡(m)\sqrt{2} \sin{\left(m \right)} 
=
= 
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\/ 2 *sin(m)
2sin⁡(m)\sqrt{2} \sin{\left(m \right)} 
sqrt(2)*sin(m)

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

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