Mister Exam

Other calculators

Solving integrals/ x-3/2x^2+5x-7

Integral of x-3/2x^2+5x-7 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                        
  /                        
 |                         
 |  /       2          \   
 |  |    3*x           |   
 |  |x - ---- + 5*x - 7| dx
 |  \     2            /   
 |                         
/                          
0
∫01((5x+(−3x22+x))−7) dx\int\limits_{0}^{1} \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx 
Integral(x - 3*x^2/2 + 5*x - 7, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

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

        ∫5x dx=5∫x dx\int 5 x\, dx = 5 \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: 5x22\frac{5 x^{2}}{2}

      1. Integrate term-by-term:

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

          ∫(−3x22) dx=−3∫x2 dx2\int \left(- \frac{3 x^{2}}{2}\right)\, dx = - \frac{3 \int x^{2}\, dx}{2}

          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: −x32- \frac{x^{3}}{2}

        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}

        The result is: −x32+x22- \frac{x^{3}}{2} + \frac{x^{2}}{2}

      The result is: −x32+3x2- \frac{x^{3}}{2} + 3 x^{2}

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

      ∫(−7) dx=−7x\int \left(-7\right)\, dx = - 7 x

    The result is: −x32+3x2−7x- \frac{x^{3}}{2} + 3 x^{2} - 7 x

  2. Now simplify:

    x(−x2+6x−14)2\frac{x \left(- x^{2} + 6 x - 14\right)}{2}

  3. Add the constant of integration:

    x(−x2+6x−14)2+constant\frac{x \left(- x^{2} + 6 x - 14\right)}{2}+ \mathrm{constant}

The answer is:

x(−x2+6x−14)2+constant\frac{x \left(- x^{2} + 6 x - 14\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                             
 |                                              
 | /       2          \                        3
 | |    3*x           |                   2   x 
 | |x - ---- + 5*x - 7| dx = C - 7*x + 3*x  - --
 | \     2            /                       2 
 |                                              
/
∫((5x+(−3x22+x))−7) dx=C−x32+3x2−7x\int \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx = C - \frac{x^{3}}{2} + 3 x^{2} - 7 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1010
Plot the graph f(x)
The answer [src] 
-9/2
−92- \frac{9}{2} 
=
= 
-9/2
−92- \frac{9}{2} 
-9/2
Numerical answer [src] 
-4.5
-4.5

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

    © Mister Exam – Calculator