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Solving integrals/ 2+sin(4*x)

Integral of 2+sin(4*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
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 |  (2 + sin(4*x)) dx
 |                   
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0
$$\int\limits_{0}^{1} \left(\sin{\left(4 x \right)} + 2\right)\, dx$$ 
Integral(2 + sin(4*x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Let .

      Then let and substitute :

      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:

      Now substitute back in:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                      
 |                               cos(4*x)
 | (2 + sin(4*x)) dx = C + 2*x - --------
 |                                  4    
/
$$\int \left(\sin{\left(4 x \right)} + 2\right)\, dx = C + 2 x - \frac{\cos{\left(4 x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
9   cos(4)
- - ------
4     4
$$\frac{9}{4} - \frac{\cos{\left(4 \right)}}{4}$$ 
=
= 
9   cos(4)
- - ------
4     4
$$\frac{9}{4} - \frac{\cos{\left(4 \right)}}{4}$$ 
9/4 - cos(4)/4
Numerical answer [src] 
2.4134109052159
2.4134109052159

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

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