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Integral of sqrt(3)*cos(x)-sin(x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                           
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 2                            
  /                           
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 |  \\/ 3 *cos(x) - sin(x)/ dx
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$$\int\limits_{0}^{\frac{\pi}{2}} \left(- \sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)\, dx$$
Integral(sqrt(3)*cos(x) - sin(x), (x, 0, pi/2))
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 times a function is the constant times the integral of the function:

      1. The integral of cosine is sine:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                      
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 | /  ___                \            ___                
 | \\/ 3 *cos(x) - sin(x)/ dx = C + \/ 3 *sin(x) + cos(x)
 |                                                       
/                                                        
$$\int \left(- \sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)\, dx = C + \sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)}$$
The graph
The answer [src]
       ___
-1 + \/ 3 
$$-1 + \sqrt{3}$$
=
=
       ___
-1 + \/ 3 
$$-1 + \sqrt{3}$$
-1 + sqrt(3)
Numerical answer [src]
0.732050807568877
0.732050807568877

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