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Solving integrals/ 8*sin(4pi*x)

Integral of 8*sin(4pi*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
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 |  8*sin(4*pi*x) dx
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0
$$\int\limits_{0}^{1} 8 \sin{\left(4 \pi x \right)}\, dx$$ 
Integral(8*sin((4*pi)*x), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    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:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
 |                        2*cos(4*pi*x)
 | 8*sin(4*pi*x) dx = C - -------------
 |                              pi     
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$$\int 8 \sin{\left(4 \pi x \right)}\, dx = C - \frac{2 \cos{\left(4 \pi x \right)}}{\pi}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
0
$$0$$ 
=
= 
0
$$0$$ 
0
Numerical answer [src] 
-2.45674672723059e-22
-2.45674672723059e-22

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

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