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dx/5+4sin(x)
Solving integrals/ dx/5+4sin(x)

Integral of dx/5+4sin(x) dx

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The solution

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∫01(4sin⁡(x)+0.2) dx\int\limits_{0}^{1} \left(4 \sin{\left(x \right)} + 0.2\right)\, dx 
Integral(0.2 + 4*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:

      ∫4sin⁡(x) dx=4∫sin⁡(x) dx\int 4 \sin{\left(x \right)}\, dx = 4 \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: −4cos⁡(x)- 4 \cos{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      ∫0.2 dx=0.2x\int 0.2\, dx = 0.2 x

    The result is: 0.2x−4cos⁡(x)0.2 x - 4 \cos{\left(x \right)}

  2. Add the constant of integration:

    0.2x−4cos⁡(x)+constant0.2 x - 4 \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

0.2x−4cos⁡(x)+constant0.2 x - 4 \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | (0.2 + 4*sin(x)) dx = C - 4*cos(x) + 0.2*x
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∫(4sin⁡(x)+0.2) dx=C+0.2x−4cos⁡(x)\int \left(4 \sin{\left(x \right)} + 0.2\right)\, dx = C + 0.2 x - 4 \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1010
Plot the graph f(x)
The answer [src] 
4.2 - 4*cos(1)
4.2−4cos⁡(1)4.2 - 4 \cos{\left(1 \right)} 
=
= 
4.2 - 4*cos(1)
4.2−4cos⁡(1)4.2 - 4 \cos{\left(1 \right)} 
4.2 - 4*cos(1)
Numerical answer [src] 
2.03879077652744
2.03879077652744
The graph
Integral of dx/5+4sin(x) dx

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

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