Mister Exam

Other calculators

Solving integrals/ xy^2dx-(y^2-x^2)

Integral of xy^2dx-(y^2-x^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  l                      
  /                      
 |                       
 |  /   2      2    2\   
 |  \x*y  + - y  + x / dx
 |                       
/                        
0
$$\int\limits_{0}^{l} \left(x y^{2} + \left(x^{2} - y^{2}\right)\right)\, dx$$ 
Integral(x*y^2 - y^2 + x^2, (x, 0, l))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of is when :

      So, the result is:

    1. Integrate term-by-term:

      1. The integral of is when :

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

      The result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                             
 |                              3    2  2       
 | /   2      2    2\          x    x *y       2
 | \x*y  + - y  + x / dx = C + -- + ----- - x*y 
 |                             3      2         
/
$$\int \left(x y^{2} + \left(x^{2} - y^{2}\right)\right)\, dx = C + \frac{x^{3}}{3} + \frac{x^{2} y^{2}}{2} - x y^{2}$$
Simplify
The answer [src] 
 3    2  2       
l    l *y       2
-- + ----- - l*y 
3      2
$$\frac{l^{3}}{3} + \frac{l^{2} y^{2}}{2} - l y^{2}$$ 
=
= 
 3    2  2       
l    l *y       2
-- + ----- - l*y 
3      2
$$\frac{l^{3}}{3} + \frac{l^{2} y^{2}}{2} - l y^{2}$$ 
l^3/3 + l^2*y^2/2 - l*y^2

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

    © Mister Exam – Calculator