Mister Exam

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Identical expressions
fifteen cos(15x-15)
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Similar expressions
15cos(15x+15)

Integral of 15cos(15x-15) dx

The solution

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

Integral(15*cos(15*x - 15), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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 | 15*cos(15*x - 15) dx = C + sin(15*x - 15)
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$$\int 15 \cos{\left(15 x - 15 \right)}\, dx = C + \sin{\left(15 x - 15 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(15)

$$\sin{\left(15 \right)}$$

sin(15)

$$\sin{\left(15 \right)}$$

sin(15)

Numerical answer [src]

0.650287840157117

0.650287840157117

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

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Integral of 15cos(15x-15) dx

Limits of integration:

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Piecewise:

The solution