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dx/2cosx+3sinx
Solving integrals/ dx/2cosx+3sinx

Integral of dx/2cosx+3sinx dx

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The solution

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∫01(3sin⁡(x)+1⋅12cos⁡(x)) dx\int\limits_{0}^{1} \left(3 \sin{\left(x \right)} + 1 \cdot \frac{1}{2} \cos{\left(x \right)}\right)\, dx 
Integral(1*cos(x)/2 + 3*sin(x), (x, 0, 1))
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:

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

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

      ∫1⋅12cos⁡(x) dx=∫cos⁡(x) dx2\int 1 \cdot \frac{1}{2} \cos{\left(x \right)}\, dx = \frac{\int \cos{\left(x \right)}\, dx}{2}

      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: sin⁡(x)2\frac{\sin{\left(x \right)}}{2}

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(3sin⁡(x)+1⋅12cos⁡(x)) dx=C+sin⁡(x)2−3cos⁡(x)\int \left(3 \sin{\left(x \right)} + 1 \cdot \frac{1}{2} \cos{\left(x \right)}\right)\, dx = C + \frac{\sin{\left(x \right)}}{2} - 3 \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
    sin(1)           
3 + ------ - 3*cos(1)
      2
−3cos⁡(1)+sin⁡(1)2+3- 3 \cos{\left(1 \right)} + \frac{\sin{\left(1 \right)}}{2} + 3 
=
= 
    sin(1)           
3 + ------ - 3*cos(1)
      2
−3cos⁡(1)+sin⁡(1)2+3- 3 \cos{\left(1 \right)} + \frac{\sin{\left(1 \right)}}{2} + 3
Упростить
Numerical answer [src] 
1.79982857479953
1.79982857479953
The graph
Integral of dx/2cosx+3sinx dx

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

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