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Solving integrals/ 2sinx-3cosx

Integral of 2sinx-3cosx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  (2*sin(x) - 3*cos(x)) dx
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∫0π4(2sin⁡(x)−3cos⁡(x)) dx\int\limits_{0}^{\frac{\pi}{4}} \left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)\, dx 
Integral(2*sin(x) - 3*cos(x), (x, 0, pi/4))
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:

      ∫2sin⁡(x) dx=2∫sin⁡(x) dx\int 2 \sin{\left(x \right)}\, dx = 2 \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: −2cos⁡(x)- 2 \cos{\left(x \right)}

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

      ∫(−3cos⁡(x)) dx=−3∫cos⁡(x) dx\int \left(- 3 \cos{\left(x \right)}\right)\, dx = - 3 \int \cos{\left(x \right)}\, dx

      1. The integral of cosine is sine:

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

      So, the result is: −3sin⁡(x)- 3 \sin{\left(x \right)}

    The result is: −3sin⁡(x)−2cos⁡(x)- 3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}

  2. Add the constant of integration:

    −3sin⁡(x)−2cos⁡(x)+constant- 3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

−3sin⁡(x)−2cos⁡(x)+constant- 3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | (2*sin(x) - 3*cos(x)) dx = C - 3*sin(x) - 2*cos(x)
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∫(2sin⁡(x)−3cos⁡(x)) dx=C−3sin⁡(x)−2cos⁡(x)\int \left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)\, dx = C - 3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}
Simplify
The graph
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750-5
Plot the graph f(x)
The answer [src] 
        ___
    5*\/ 2 
2 - -------
       2
2−5222 - \frac{5 \sqrt{2}}{2} 
=
= 
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    5*\/ 2 
2 - -------
       2
2−5222 - \frac{5 \sqrt{2}}{2} 
2 - 5*sqrt(2)/2
Numerical answer [src] 
-1.53553390593274
-1.53553390593274

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

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