Integral of 2sinx-cosx dx

The solution

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 pi                       
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 |  (2*sin(x) - cos(x)) dx
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$$\int\limits_{0}^{\pi} \left(2 \sin{\left(x \right)} - \cos{\left(x \right)}\right)\, dx$$

Integral(2*sin(x) - cos(x), (x, 0, pi))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(x \right)}\, dx = 2 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \cos{\left(x \right)}\right)\, dx = - \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $- \sin{\left(x \right)}$
The result is: $- \sin{\left(x \right)} - 2 \cos{\left(x \right)}$
Add the constant of integration:

$- \sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- \sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | (2*sin(x) - cos(x)) dx = C - sin(x) - 2*cos(x)
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$$\int \left(2 \sin{\left(x \right)} - \cos{\left(x \right)}\right)\, dx = C - \sin{\left(x \right)} - 2 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

Numerical answer [src]

4.0

4.0

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

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Integral of 2sinx-cosx dx

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The solution