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Integral of -3ysinx+12ycosx dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
 2*pi                              
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  |  (-3*y*sin(x) + 12*y*cos(x)) dx
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$$\int\limits_{0}^{2 \pi} \left(- 3 y \sin{\left(x \right)} + 12 y \cos{\left(x \right)}\right)\, dx$$
Integral((-3*y)*sin(x) + (12*y)*cos(x), (x, 0, 2*pi))
Detail solution
  1. Integrate term-by-term:

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

      1. The integral of sine is negative cosine:

      So, the result is:

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

      1. The integral of cosine is sine:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                             
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 | (-3*y*sin(x) + 12*y*cos(x)) dx = C + 3*y*cos(x) + 12*y*sin(x)
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$$\int \left(- 3 y \sin{\left(x \right)} + 12 y \cos{\left(x \right)}\right)\, dx = C + 12 y \sin{\left(x \right)} + 3 y \cos{\left(x \right)}$$
The answer [src]
0
$$0$$
=
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0
$$0$$
0

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