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Solving integrals/ dx/2sinx+cosx

Integral of dx/2sinx+cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                         
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 |  (0.5*sin(x) + cos(x)) dx
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0
$$\int\limits_{0}^{1} \left(0.5 \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$ 
Integral(0.5*sin(x) + cos(x), (x, 0, 1))
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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 | (0.5*sin(x) + cos(x)) dx = C - 0.5*cos(x) + sin(x)
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$$\int \left(0.5 \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - 0.5 \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
0.5 - 0.5*cos(1) + sin(1)
$$- 0.5 \cos{\left(1 \right)} + 0.5 + \sin{\left(1 \right)}$$ 
=
= 
0.5 - 0.5*cos(1) + sin(1)
$$- 0.5 \cos{\left(1 \right)} + 0.5 + \sin{\left(1 \right)}$$ 
0.5 - 0.5*cos(1) + sin(1)
Numerical answer [src] 
1.07131983187383
1.07131983187383

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

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