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Solving integrals/ y*sin(x)

Integral of y*sin(x) dx

Limits of integration:

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The solution

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∫03ysin⁡(x) dx\int\limits_{0}^{3} y \sin{\left(x \right)}\, dx 
Integral(y*sin(x), (x, 0, 3))
Detail solution

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

    ∫ysin⁡(x) dx=y∫sin⁡(x) dx\int y \sin{\left(x \right)}\, dx = y \int \sin{\left(x \right)}\, dx

    1. The integral of sine is negative cosine:

      ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

    So, the result is: −ycos⁡(x)- y \cos{\left(x \right)}

  2. Add the constant of integration:

    −ycos⁡(x)+constant- y \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

−ycos⁡(x)+constant- y \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫ysin⁡(x) dx=C−ycos⁡(x)\int y \sin{\left(x \right)}\, dx = C - y \cos{\left(x \right)}
Simplify
The answer [src] 
y - y*cos(3)
−ycos⁡(3)+y- y \cos{\left(3 \right)} + y 
=
= 
y - y*cos(3)
−ycos⁡(3)+y- y \cos{\left(3 \right)} + y 
y - y*cos(3)

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

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