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Solving integrals/ 3sin(t)-2cos(t)

Integral of 3sin(t)-2cos(t) dt

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 3/2                        
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 |  (3*sin(t) - 2*cos(t)) dt
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$$\int\limits_{0}^{\frac{3}{2}} \left(3 \sin{\left(t \right)} - 2 \cos{\left(t \right)}\right)\, dt$$ 
Integral(3*sin(t) - 2*cos(t), (t, 0, 3/2))
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. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
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 | (3*sin(t) - 2*cos(t)) dt = C - 3*cos(t) - 2*sin(t)
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$$\int \left(3 \sin{\left(t \right)} - 2 \cos{\left(t \right)}\right)\, dt = C - 2 \sin{\left(t \right)} - 3 \cos{\left(t \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3 - 3*cos(3/2) - 2*sin(3/2)
$$- 2 \sin{\left(\frac{3}{2} \right)} - 3 \cos{\left(\frac{3}{2} \right)} + 3$$ 
=
= 
3 - 3*cos(3/2) - 2*sin(3/2)
$$- 2 \sin{\left(\frac{3}{2} \right)} - 3 \cos{\left(\frac{3}{2} \right)} + 3$$ 
3 - 3*cos(3/2) - 2*sin(3/2)
Numerical answer [src] 
0.792798421788782
0.792798421788782

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

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