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Solving integrals/ cos(3*x-pi/4)

Integral of cos(3*x-pi/4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                 
  /                 
 |                  
 |     /      pi\   
 |  cos|3*x - --| dx
 |     \      4 /   
 |                  
/                   
pi                  
--                  
4
$$\int\limits_{\frac{\pi}{4}}^{\pi} \cos{\left(3 x - \frac{\pi}{4} \right)}\, dx$$ 
Integral(cos(3*x - pi/4), (x, pi/4, pi))
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 cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          /      pi\
 |                        sin|3*x - --|
 |    /      pi\             \      4 /
 | cos|3*x - --| dx = C + -------------
 |    \      4 /                3      
 |                                     
/
$$\int \cos{\left(3 x - \frac{\pi}{4} \right)}\, dx = C + \frac{\sin{\left(3 x - \frac{\pi}{4} \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ___
  1   \/ 2 
- - + -----
  3     6
$$- \frac{1}{3} + \frac{\sqrt{2}}{6}$$ 
=
= 
        ___
  1   \/ 2 
- - + -----
  3     6
$$- \frac{1}{3} + \frac{\sqrt{2}}{6}$$ 
-1/3 + sqrt(2)/6
Numerical answer [src] 
-0.0976310729378174
-0.0976310729378174

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

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