Mister Exam

Other calculators

x-3
Solving integrals/ x-3

Integral of x-3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

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

      ∫(−3) dx=−3x\int \left(-3\right)\, dx = - 3 x

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                  2      
 |                  x       
 | (x - 3) dx = C + -- - 3*x
 |                  2       
/
∫(x−3) dx=C+x22−3x\int \left(x - 3\right)\, dx = C + \frac{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] 
-5/2
−52- \frac{5}{2} 
=
= 
-5/2
−52- \frac{5}{2} 
-5/2
Numerical answer [src] 
-2.5
-2.5
The graph
Integral of x-3 dx

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

    © Mister Exam – Calculator