Integral of sin15x dx

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  1             
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 |  sin(15*x) dx
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0

\int\limits_{0}^{1} \sin{\left(15 x \right)}\, dx

Integral(sin(15*x), (x, 0, 1))

Detail solution

Let $u = 15 x$ .

Then let $du = 15 dx$ and substitute $\frac{du}{15}$ :

$\int \frac{\sin{\left(u \right)}}{15}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{15}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{15}$
Now substitute $u$ back in:

$- \frac{\cos{\left(15 x \right)}}{15}$
Add the constant of integration:

$- \frac{\cos{\left(15 x \right)}}{15}+ \mathrm{constant}$

The answer is:

- \frac{\cos{\left(15 x \right)}}{15}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                            
 |                    cos(15*x)
 | sin(15*x) dx = C - ---------
 |                        15   
/

\int \sin{\left(15 x \right)}\, dx = C - \frac{\cos{\left(15 x \right)}}{15}

Simplify

The graph

Plot the graph f(x)

The answer [src]

1    cos(15)
-- - -------
15      15

\frac{1}{15} - \frac{\cos{\left(15 \right)}}{15}

1    cos(15)
-- - -------
15      15

\frac{1}{15} - \frac{\cos{\left(15 \right)}}{15}

1/15 - cos(15)/15

Numerical answer [src]

0.117312527523921

0.117312527523921

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