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Solving integrals/ sin(x+pi/4)

Integral of sin(x+pi/4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

    1. The integral of sine is negative cosine:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                                 
 |    /    pi\             /    pi\
 | sin|x + --| dx = C - cos|x + --|
 |    \    4 /             \    4 /
 |                                 
/
$$\int \sin{\left(x + \frac{\pi}{4} \right)}\, dx = C - \cos{\left(x + \frac{\pi}{4} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___
\/ 2 
-----
  2
$$\frac{\sqrt{2}}{2}$$ 
=
= 
  ___
\/ 2 
-----
  2
$$\frac{\sqrt{2}}{2}$$ 
sqrt(2)/2
Numerical answer [src] 
0.707106781186547
0.707106781186547

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

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