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Solving integrals/ 2*sin(x)

Integral of 2*sin(x) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  2*sin(x) dx
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∫0p32sin⁡(x) dx\int\limits_{0}^{\frac{p}{3}} 2 \sin{\left(x \right)}\, dx 
Integral(2*sin(x), (x, 0, p/3))
Detail solution

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

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

    1. The integral of sine is negative cosine:

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

    So, the result is: −2cos⁡(x)- 2 \cos{\left(x \right)}

  2. Add the constant of integration:

    −2cos⁡(x)+constant- 2 \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

−2cos⁡(x)+constant- 2 \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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 | 2*sin(x) dx = C - 2*cos(x)
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∫2sin⁡(x) dx=C−2cos⁡(x)\int 2 \sin{\left(x \right)}\, dx = C - 2 \cos{\left(x \right)}
Simplify
The answer [src] 
         /p\
2 - 2*cos|-|
         \3/
2−2cos⁡(p3)2 - 2 \cos{\left(\frac{p}{3} \right)} 
=
= 
         /p\
2 - 2*cos|-|
         \3/
2−2cos⁡(p3)2 - 2 \cos{\left(\frac{p}{3} \right)} 
2 - 2*cos(p/3)

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

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