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Integral of d{x}:
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Integral of sin(7x−(pi/4))
Identical expressions
sin(7x−(pi/ four))
sinus of (7x−( Pi divide by 4))
sinus of (7x−( Pi divide by four))
sin7x−pi/4
sin(7x−(pi divide by 4))
sin(7x−(pi/4))dx

Solving integrals/ sin(7x−(pi/4))

Integral of sin(7x−(pi/4)) dx

The solution

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  1                 
  /                 
 |                  
 |     /      pi\   
 |  sin|7*x - --| dx
 |     \      4 /   
 |                  
/                   
0

$$\int\limits_{0}^{1} \sin{\left(7 x - \frac{\pi}{4} \right)}\, dx$$

Integral(sin(7*x - pi/4), (x, 0, 1))

Detail solution

Let $u = 7 x - \frac{\pi}{4}$ .

Then let $du = 7 dx$ and substitute $\frac{du}{7}$ :

$\int \frac{\sin{\left(u \right)}}{49}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{7}\, du = \frac{\int \sin{\left(u \right)}\, du}{7}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{7}$
Now substitute $u$ back in:

$- \frac{\cos{\left(7 x - \frac{\pi}{4} \right)}}{7}$
Now simplify:

$- \frac{\sin{\left(7 x + \frac{\pi}{4} \right)}}{7}$
Add the constant of integration:

$- \frac{\sin{\left(7 x + \frac{\pi}{4} \right)}}{7}+ \mathrm{constant}$

The answer is:

$- \frac{\sin{\left(7 x + \frac{\pi}{4} \right)}}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          /      pi\
 |                        cos|7*x - --|
 |    /      pi\             \      4 /
 | sin|7*x - --| dx = C - -------------
 |    \      4 /                7      
 |                                     
/

$$-{{\cos \left(7\,x-{{\pi}\over{4}}\right)}\over{7}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     /    pi\        
  sin|7 + --|     ___
     \    4 /   \/ 2 
- ----------- + -----
       7          14

$${{\cos \left({{\pi}\over{4}}\right)}\over{7}}-{{\cos \left({{\pi-28 }\over{4}}\right)}\over{7}}$$

     /    pi\        
  sin|7 + --|     ___
     \    4 /   \/ 2 
- ----------- + -----
       7          14

$$- \frac{\sin{\left(\frac{\pi}{4} + 7 \right)}}{7} + \frac{\sqrt{2}}{14}$$

Simplify

Numerical answer [src]

-0.0415060420448813

-0.0415060420448813

The graph

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

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Identical expressions

Integral of sin(7x−(pi/4)) dx

Limits of integration:

The graph:

Piecewise:

The solution