Integral of y*sin(x) dx

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$$\int\limits_{0}^{3} y \sin{\left(x \right)}\, dx$$

Integral(y*sin(x), (x, 0, 3))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The answer [src]

y - y*cos(3)

$$- y \cos{\left(3 \right)} + y$$

y - y*cos(3)

$$- y \cos{\left(3 \right)} + y$$

y - y*cos(3)

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