Integral of sin(7x) dx

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  1            
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 |  sin(7*x) dx
 |             
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0

\int\limits_{0}^{1} \sin{\left(7 x \right)}\, dx

Integral(sin(7*x), (x, 0, 1))

Detail solution

Let $u = 7 x$ .

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

$\int \frac{\sin{\left(u \right)}}{7}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{7}$
  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:

$- \frac{\cos{\left(7 x \right)}}{7}$
Add the constant of integration:

$- \frac{\cos{\left(7 x \right)}}{7}+ \mathrm{constant}$

The answer is:

- \frac{\cos{\left(7 x \right)}}{7}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                          
 |                   cos(7*x)
 | sin(7*x) dx = C - --------
 |                      7    
/

\int \sin{\left(7 x \right)}\, dx = C - \frac{\cos{\left(7 x \right)}}{7}

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   cos(7)
- - ------
7     7

\frac{1}{7} - \frac{\cos{\left(7 \right)}}{7}

1   cos(7)
- - ------
7     7

\frac{1}{7} - \frac{\cos{\left(7 \right)}}{7}

1/7 - cos(7)/7

Numerical answer [src]

0.0351568208080993

0.0351568208080993

The graph

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