Mister Exam

Integral of 2sinx+cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                       
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 |  (2*sin(x) + cos(x)) dx
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0                         
$$\int\limits_{0}^{\pi} \left(2 \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$
Integral(2*sin(x) + cos(x), (x, 0, pi))
Detail solution
  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 cosine is sine:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                              
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 | (2*sin(x) + cos(x)) dx = C - 2*cos(x) + sin(x)
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$$\int \left(2 \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - 2 \cos{\left(x \right)}$$
The graph
The answer [src]
4
$$4$$
=
=
4
$$4$$
4
Numerical answer [src]
4.0
4.0

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