Mister Exam

Lang:

Integral of xx+yy dy

You have entered [src]

  1               
  /               
 |                
 |  (x*x + y*y) dy
 |                
/                 
0

$$\int\limits_{0}^{1} \left(x x + y y\right)\, dy$$

Integral(x*x + y*y, (y, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int x x\, dy = x^{2} y$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{y^{2}}{2}$
The result is: $x^{2} y + \frac{y^{2}}{2}$
Now simplify:

$\frac{y \left(2 x^{2} + y\right)}{2}$
Add the constant of integration:

$\frac{y \left(2 x^{2} + y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{y \left(2 x^{2} + y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      2       
 |                      y       2
 | (x*x + y*y) dy = C + -- + y*x 
 |                      2        
/

$$\int \left(x x + y y\right)\, dy = C + x^{2} y + \frac{y^{2}}{2}$$

Simplify

The answer [src]

1    2
- + x 
3

$$x^{2} + \frac{1}{3}$$

1    2
- + x 
3

$$x^{2} + \frac{1}{3}$$

1/3 + x^2

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

Integral of x*x+y*y dy