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Solving integrals/ sin(4*x+3*pi/8)

Integral of sin(4*x+3*pi/8) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 9*pi                  
 ----                  
  32                   
   /                   
  |                    
  |     /      3*pi\   
  |  sin|4*x + ----| dx
  |     \       8  /   
  |                    
 /                     
 pi                    
 --                    
 32
$$\int\limits_{\frac{\pi}{32}}^{\frac{9 \pi}{32}} \sin{\left(4 x + \frac{3 \pi}{8} \right)}\, dx$$ 
Integral(sin(4*x + (3*pi)/8), (x, pi/32, 9*pi/32))
Detail solution

  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:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            /      3*pi\
 |                          cos|4*x + ----|
 |    /      3*pi\             \       8  /
 | sin|4*x + ----| dx = C - ---------------
 |    \       8  /                 4       
 |                                         
/
$$\int \sin{\left(4 x + \frac{3 \pi}{8} \right)}\, dx = C - \frac{\cos{\left(4 x + \frac{3 \pi}{8} \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
0
$$0$$ 
=
= 
0
$$0$$ 
0
Numerical answer [src] 
3.82701278282084e-17
3.82701278282084e-17

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

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