Mister Exam

Other calculators

Solving integrals/ x^2-7x

Integral of x^2-7x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3              
  /              
 |               
 |  / 2      \   
 |  \x  - 7*x/ dx
 |               
/                
2
∫23(x2−7x) dx\int\limits_{2}^{3} \left(x^{2} - 7 x\right)\, dx 
Integral(x^2 - 7*x, (x, 2, 3))
Detail solution

  1. Integrate term-by-term:

    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}

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

      ∫(−7x) dx=−7∫x dx\int \left(- 7 x\right)\, dx = - 7 \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: −7x22- \frac{7 x^{2}}{2}

    The result is: x33−7x22\frac{x^{3}}{3} - \frac{7 x^{2}}{2}

  2. Now simplify:

    x2(2x−21)6\frac{x^{2} \left(2 x - 21\right)}{6}

  3. Add the constant of integration:

    x2(2x−21)6+constant\frac{x^{2} \left(2 x - 21\right)}{6}+ \mathrm{constant}

The answer is:

x2(2x−21)6+constant\frac{x^{2} \left(2 x - 21\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                        2    3
 | / 2      \          7*x    x 
 | \x  - 7*x/ dx = C - ---- + --
 |                      2     3 
/
∫(x2−7x) dx=C+x33−7x22\int \left(x^{2} - 7 x\right)\, dx = C + \frac{x^{3}}{3} - \frac{7 x^{2}}{2}
Simplify
The graph
2.003.002.102.202.302.402.502.602.702.802.900-30
Plot the graph f(x)
The answer [src] 
-67/6
−676- \frac{67}{6} 
=
= 
-67/6
−676- \frac{67}{6} 
-67/6
Numerical answer [src] 
-11.1666666666667
-11.1666666666667

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

    © Mister Exam – Calculator