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Solving integrals/ sqrt2-2sin(x)

Integral of sqrt2-2sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
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 3                       
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 |  \\/ 2  - 2*sin(x)/ dx
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0
$$\int\limits_{0}^{\frac{\pi}{3}} \left(- 2 \sin{\left(x \right)} + \sqrt{2}\right)\, dx$$ 
Integral(sqrt(2) - 2*sin(x), (x, 0, pi/3))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of sine is negative cosine:

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                              
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 | /  ___           \                         ___
 | \\/ 2  - 2*sin(x)/ dx = C + 2*cos(x) + x*\/ 2 
 |                                               
/
$$\int \left(- 2 \sin{\left(x \right)} + \sqrt{2}\right)\, dx = C + \sqrt{2} x + 2 \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          ___
     pi*\/ 2 
-1 + --------
        3
$$-1 + \frac{\sqrt{2} \pi}{3}$$ 
=
= 
          ___
     pi*\/ 2 
-1 + --------
        3
$$-1 + \frac{\sqrt{2} \pi}{3}$$ 
-1 + pi*sqrt(2)/3
Numerical answer [src] 
0.480960979386122
0.480960979386122

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

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