Mister Exam

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Integral of d{x}:
Integral of (-1+u)/(1+u^2)
Integral of y/sqrt(1+y^2)
Integral of (-1)^x
Integral of (xe^x)dx
Identical expressions
xy^ two / two
xy squared divide by 2
xy to the power of two divide by two
xy2/2
xy²/2
xy to the power of 2/2
xy^2 divide by 2
xy^2/2dx
What you mean?
x*y^2/2
x*y^1
x*y^2/2
x*y*2/2
x*y*2/2

You entered:

xy^2/2

What you mean?

x*y^2/2

x*y^1

x*y^2/2

x*y*2/2

x*y*2/2

Integral of xy^2/2 dx

The solution

You have entered [src]

$$\int\limits_{0}^{2} \frac{x y^{2}}{2}\, dx$$

Integral(x*y^2/2, (x, 0, 2))

Detail solution

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

$\int \frac{x y^{2}}{2}\, dx = \frac{y^{2} \int x\, dx}{2}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
So, the result is: $\frac{x^{2} y^{2}}{4}$
Add the constant of integration:

$\frac{x^{2} y^{2}}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} y^{2}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
 |                    
 |    2           2  2
 | x*y           x *y 
 | ---- dx = C + -----
 |  2              4  
 |                    
/

$${{x^2\,y^2}\over{4}}$$

Simplify

The answer [src]

2
y

$$y^2$$

2
y

$$y^{2}$$

Simplify

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

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What you mean?

Integral of xy^2/2 dx

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Piecewise:

The solution