Integral of sin(x-1) dx

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 pi              
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 |  sin(x - 1) dx
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-pi

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

Integral(sin(x - 1), (x, -pi, pi))

Detail solution

Let $u = x - 1$ .

Then let $du = dx$ and substitute $du$ :

$\int \sin{\left(u \right)}\, du$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
Now substitute $u$ back in:

$- \cos{\left(x - 1 \right)}$
Now simplify:

$- \cos{\left(x - 1 \right)}$
Add the constant of integration:

$- \cos{\left(x - 1 \right)}+ \mathrm{constant}$

The answer is:

$- \cos{\left(x - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | sin(x - 1) dx = C - cos(x - 1)
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$$\int \sin{\left(x - 1 \right)}\, dx = C - \cos{\left(x - 1 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

-2.06493225255183e-16

-2.06493225255183e-16

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