Integral of 5*sin(xdx) dx

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$$\int\limits_{0}^{4} 5 \sin{\left(x \right)}\, dx$$

Integral(5*sin(x), (x, 0, 4))

Detail solution

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

$\int 5 \sin{\left(x \right)}\, dx = 5 \int \sin{\left(x \right)}\, dx$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
So, the result is: $- 5 \cos{\left(x \right)}$
Add the constant of integration:

$- 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 5*sin(x) dx = C - 5*cos(x)
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$$\int 5 \sin{\left(x \right)}\, dx = C - 5 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5 - 5*cos(4)

$$5 - 5 \cos{\left(4 \right)}$$

5 - 5*cos(4)

$$5 - 5 \cos{\left(4 \right)}$$

5 - 5*cos(4)

Numerical answer [src]

8.26821810431806

8.26821810431806

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