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Solving integrals/ (4sinx+2cosx)

Integral of (4sinx+2cosx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                         
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 |  (4*sin(x) + 2*cos(x)) dx
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$$\int\limits_{0}^{\frac{\pi}{2}} \left(4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)\, dx$$ 
Integral(4*sin(x) + 2*cos(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. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
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 | (4*sin(x) + 2*cos(x)) dx = C - 4*cos(x) + 2*sin(x)
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$$\int \left(4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)\, dx = C + 2 \sin{\left(x \right)} - 4 \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
6
$$6$$ 
=
= 
6
$$6$$ 
6
Numerical answer [src] 
6.0
6.0

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

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