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Solving integrals/ cos(x+pi/4)

Integral of cos(x+pi/4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi               
  /               
 |                
 |     /    pi\   
 |  cos|x + --| dx
 |     \    4 /   
 |                
/                 
pi                
--                
2
$$\int\limits_{\frac{\pi}{2}}^{\pi} \cos{\left(x + \frac{\pi}{4} \right)}\, dx$$ 
Integral(cos(x + pi/4), (x, pi/2, pi))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of cosine is sine:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                                 
 |    /    pi\             /    pi\
 | cos|x + --| dx = C + sin|x + --|
 |    \    4 /             \    4 /
 |                                 
/
$$\int \cos{\left(x + \frac{\pi}{4} \right)}\, dx = C + \sin{\left(x + \frac{\pi}{4} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   ___
-\/ 2
$$- \sqrt{2}$$ 
=
= 
   ___
-\/ 2
$$- \sqrt{2}$$ 
-sqrt(2)
Numerical answer [src] 
-1.41421356237309
-1.41421356237309

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

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