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Integral of d{x}:
Integral of sinx
Integral of sin(x²)
Integral of -(x^2)/2
Integral of (x^2-1)/(x^3+x)
Derivative of:
-(x^2)/2
Identical expressions
-(x^ two)/ two
minus (x squared ) divide by 2
minus (x to the power of two) divide by two
-(x2)/2
-x2/2
-(x²)/2
-(x to the power of 2)/2
-x^2/2
-(x^2) divide by 2
-(x^2)/2dx
Similar expressions
e^(-x^2/2)
x^2*exp(-x^2/2)
-x^(2)/2+3*x+6
(x^2)/2

Solving integrals/ -(x^2)/2

Integral of -(x^2)/2 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{\left(-1\right) x^{2}}{2}\, dx$$

Integral((-x^2)/2, (x, 0, 1))

Detail solution

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

$\int \frac{\left(-1\right) x^{2}}{2}\, dx = \frac{\int \left(- x^{2}\right)\, dx}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
So, the result is: $- \frac{x^{3}}{6}$
Add the constant of integration:

$- \frac{x^{3}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{x^{3}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                
 |                 
 |   2            3
 | -x            x 
 | ---- dx = C - --
 |  2            6 
 |                 
/

$$\int \frac{\left(-1\right) x^{2}}{2}\, dx = C - \frac{x^{3}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/6

$$- \frac{1}{6}$$

=

-1/6

$$- \frac{1}{6}$$

-1/6

Numerical answer [src]

-0.166666666666667

-0.166666666666667

The graph

Integral of -(x^2)/2 dx

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