Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^x/x^2
Integral of sin(x)^2*cos(x)^4
Integral of x*ln(x+1)dx
Integral of 1/(2-x)
Identical expressions
y^ two +z^ two
y squared plus z squared
y to the power of two plus z to the power of two
y2+z2
y²+z²
y to the power of 2+z to the power of 2
Similar expressions
y^2-z^2

Integral of y^2+z^2 dy

The solution

You have entered [src]

 1 - z            
   /              
  |               
  |   / 2    2\   
  |   \y  + z / dy
  |               
 /                
 0

$$\int\limits_{0}^{1 - z} \left(y^{2} + z^{2}\right)\, dy$$

Integral(y^2 + z^2, (y, 0, 1 - z))

Detail solution

Integrate term-by-term:
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y^{2}\, dy = \frac{y^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int z^{2}\, dy = y z^{2}$
The result is: $\frac{y^{3}}{3} + y z^{2}$
Now simplify:

$y \left(\frac{y^{2}}{3} + z^{2}\right)$
Add the constant of integration:

$y \left(\frac{y^{2}}{3} + z^{2}\right)+ \mathrm{constant}$

The answer is:

$y \left(\frac{y^{2}}{3} + z^{2}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                     3       
 | / 2    2\          y       2
 | \y  + z / dy = C + -- + y*z 
 |                    3        
/

$$\int \left(y^{2} + z^{2}\right)\, dy = C + \frac{y^{3}}{3} + y z^{2}$$

Simplify

The answer [src]

       3             
(1 - z)     2        
-------- + z *(1 - z)
   3

$$z^{2} \left(1 - z\right) + \frac{\left(1 - z\right)^{3}}{3}$$

       3             
(1 - z)     2        
-------- + z *(1 - z)
   3

$$z^{2} \left(1 - z\right) + \frac{\left(1 - z\right)^{3}}{3}$$

(1 - z)^3/3 + z^2*(1 - z)

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of y^2+z^2 dy

Limits of integration:

The graph:

Piecewise:

The solution