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Canonical form:
x^2/a^2+y^2/b^2
Identical expressions
x^ two /a^ two +y^ two /b^ two
x squared divide by a squared plus y squared divide by b squared
x to the power of two divide by a to the power of two plus y to the power of two divide by b to the power of two
x2/a2+y2/b2
x²/a²+y²/b²
x to the power of 2/a to the power of 2+y to the power of 2/b to the power of 2
x^2 divide by a^2+y^2 divide by b^2
x^2/a^2+y^2/b^2dx
Similar expressions
x^2/a^2-y^2/b^2

Integral of x^2/a^2+y^2/b^2 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |  / 2    2\   
 |  |x    y |   
 |  |-- + --| dx
 |  | 2    2|   
 |  \a    b /   
 |              
/               
0

$$\int\limits_{0}^{1} \left(\frac{y^{2}}{b^{2}} + \frac{x^{2}}{a^{2}}\right)\, dx$$

Integral(x^2/a^2 + y^2/b^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{y^{2}}{b^{2}}\, dx = \frac{x y^{2}}{b^{2}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x^{2}}{a^{2}}\, dx = \frac{\int x^{2}\, dx}{a^{2}}$
  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: $\frac{x^{3}}{3 a^{2}}$
The result is: $\frac{x y^{2}}{b^{2}} + \frac{x^{3}}{3 a^{2}}$
Add the constant of integration:

$\frac{x y^{2}}{b^{2}} + \frac{x^{3}}{3 a^{2}}+ \mathrm{constant}$

The answer is:

$\frac{x y^{2}}{b^{2}} + \frac{x^{3}}{3 a^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 | / 2    2\            3       2
 | |x    y |           x     x*y 
 | |-- + --| dx = C + ---- + ----
 | | 2    2|             2     2 
 | \a    b /          3*a     b  
 |                               
/

$$\int \left(\frac{y^{2}}{b^{2}} + \frac{x^{2}}{a^{2}}\right)\, dx = C + \frac{x y^{2}}{b^{2}} + \frac{x^{3}}{3 a^{2}}$$

Simplify

The answer [src]

        2
 1     y 
---- + --
   2    2
3*a    b

$$\frac{y^{2}}{b^{2}} + \frac{1}{3 a^{2}}$$

        2
 1     y 
---- + --
   2    2
3*a    b

$$\frac{y^{2}}{b^{2}} + \frac{1}{3 a^{2}}$$

1/(3*a^2) + y^2/b^2

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

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Integral of x^2/a^2+y^2/b^2 dx

Limits of integration:

The graph:

Piecewise:

The solution