Mister Exam

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How to use it?
Integral of d{x}:
Integral of xy^2
Integral of Sin^5*x/2*cos*x/2
Integral of log2x
Integral of e^(x-y)
Plot:
xy^2
The double integral of:
xy^2
xy^2
Identical expressions
xy^ two
xy squared
xy to the power of two
xy2
xy²
xy to the power of 2
xy^2dx

Solving integrals/ xy^2

Integral of xy^2 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} x y^{2}\, dx$$

Simplify

Detail solution

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

$\int x y^{2}\, dx = y^{2} \int x\, dx$
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: $\frac{x^{2} y^{2}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

 2
y 
--
2

$${{y^2}\over{2}}$$

=

 2
y 
--
2

$$\frac{y^{2}}{2}$$

Simplify

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