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Integral of (3-2x)⁴dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1              
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 |           4   
 |  (3 - 2*x)  dx
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0                
$$\int\limits_{0}^{1} \left(3 - 2 x\right)^{4}\, dx$$
Integral((3 - 2*x)^4, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. 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 is when :

        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 is when :

        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 is when :

        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 is when :

        So, the result is:

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

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                              
 |                              5
 |          4          (3 - 2*x) 
 | (3 - 2*x)  dx = C - ----------
 |                         10    
/                                
$$\int \left(3 - 2 x\right)^{4}\, dx = C - \frac{\left(3 - 2 x\right)^{5}}{10}$$
The graph
The answer [src]
121/5
$$\frac{121}{5}$$
=
=
121/5
$$\frac{121}{5}$$
121/5
Numerical answer [src]
24.2
24.2

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