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Solving integrals/ 3x-3/√1-x²dx

Integral of 3x-3/√1-x²dx dx

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Piecewise:

The solution

You have entered [src] 
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 |  /        3      2\   
 |  |3*x - ----- - x | dx
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∫01(−x2+(3x−31)) dx\int\limits_{0}^{1} \left(- x^{2} + \left(3 x - \frac{3}{\sqrt{1}}\right)\right)\, dx 
Integral(3*x - 3 - x^2, (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:

      ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: −x33- \frac{x^{3}}{3}

    1. Integrate term-by-term:

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

        ∫3x dx=3∫x dx\int 3 x\, dx = 3 \int x\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

        So, the result is: 3x22\frac{3 x^{2}}{2}

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

        ∫(−31) dx=−3x\int \left(- \frac{3}{\sqrt{1}}\right)\, dx = - 3 x

      The result is: 3x22−3x\frac{3 x^{2}}{2} - 3 x

    The result is: −x33+3x22−3x- \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - 3 x

  2. Now simplify:

    x(−2x2+9x−18)6\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}

  3. Add the constant of integration:

    x(−2x2+9x−18)6+constant\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}+ \mathrm{constant}

The answer is:

x(−2x2+9x−18)6+constant\frac{x \left(- 2 x^{2} + 9 x - 18\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                           
 |                                    3      2
 | /        3      2\                x    3*x 
 | |3*x - ----- - x | dx = C - 3*x - -- + ----
 | |        ___     |                3     2  
 | \      \/ 1      /                         
 |                                            
/
∫(−x2+(3x−31)) dx=C−x33+3x22−3x\int \left(- x^{2} + \left(3 x - \frac{3}{\sqrt{1}}\right)\right)\, dx = C - \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - 3 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
-11/6
−116- \frac{11}{6} 
=
= 
-11/6
−116- \frac{11}{6} 
-11/6
Numerical answer [src] 
-1.83333333333333
-1.83333333333333

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

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