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Solving integrals/ 4cosx-3sinx

Integral of 4cosx-3sinx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

      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] 
  /                                                  
 |                                                   
 | (4*cos(x) - 3*sin(x)) dx = C + 3*cos(x) + 4*sin(x)
 |                                                   
/
$$4\,\sin x+3\,\cos x$$
Simplify
The answer [src] 
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    7*\/ 2 
4 - -------
       2
$$4\,\sin \left({{\pi}\over{2}}\right)+3\,\cos \left({{\pi}\over{2}} \right)-4\,\sin \left({{\pi}\over{4}}\right)-3\,\cos \left({{\pi }\over{4}}\right)$$ 
=
= 
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    7*\/ 2 
4 - -------
       2
$$4 - \frac{7 \sqrt{2}}{2}$$
Упростить
Numerical answer [src] 
-0.949747468305832
-0.949747468305832

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

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