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Solving integrals/ (80cosx)*(sin^3(x))

Integral of (80cosx)*(sin^3(x)) dx

Limits of integration:

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The solution

You have entered [src] 
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∫0π4sin⁡3(x)80cos⁡(x) dx\int\limits_{0}^{\frac{\pi}{4}} \sin^{3}{\left(x \right)} 80 \cos{\left(x \right)}\, dx 
Integral((80*cos(x))*sin(x)^3, (x, 0, pi/4))
Detail solution

  1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

    Then let du=cos⁡(x)dxdu = \cos{\left(x \right)} dx and substitute 80du80 du:

    ∫80u3 du\int 80 u^{3}\, du

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

      ∫u3 du=80∫u3 du\int u^{3}\, du = 80 \int u^{3}\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u3 du=u44\int u^{3}\, du = \frac{u^{4}}{4}

      So, the result is: 20u420 u^{4}

    Now substitute uu back in:

    20sin⁡4(x)20 \sin^{4}{\left(x \right)}

  2. Add the constant of integration:

    20sin⁡4(x)+constant20 \sin^{4}{\left(x \right)}+ \mathrm{constant}

The answer is:

20sin⁡4(x)+constant20 \sin^{4}{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | 80*cos(x)*sin (x) dx = C + 20*sin (x)
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∫sin⁡3(x)80cos⁡(x) dx=C+20sin⁡4(x)\int \sin^{3}{\left(x \right)} 80 \cos{\left(x \right)}\, dx = C + 20 \sin^{4}{\left(x \right)}
Simplify
The graph
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75040
Plot the graph f(x)
The answer [src] 
5
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5
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Numerical answer [src] 
5.0
5.0

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

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