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Similar expressions
(3(x-2y^2))/4

Integral of (3(x+2y^2))/4 dz

The solution

You have entered [src]

  z                
  /                
 |                 
 |    /       2\   
 |  3*\x + 2*y /   
 |  ------------ dz
 |       4         
 |                 
/                  
1

$$\int\limits_{1}^{z} \frac{3 \left(x + 2 y^{2}\right)}{4}\, dz$$

Integral((3*(x + 2*y^2))/4, (z, 1, z))

Detail solution

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

$\int \frac{3 \left(x + 2 y^{2}\right)}{4}\, dz = \frac{3 z \left(x + 2 y^{2}\right)}{4}$
Add the constant of integration:

$\frac{3 z \left(x + 2 y^{2}\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{3 z \left(x + 2 y^{2}\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 |   /       2\              /       2\
 | 3*\x + 2*y /          3*z*\x + 2*y /
 | ------------ dz = C + --------------
 |      4                      4       
 |                                     
/

$$\int \frac{3 \left(x + 2 y^{2}\right)}{4}\, dz = C + \frac{3 z \left(x + 2 y^{2}\right)}{4}$$

Simplify

The answer [src]

     2           /   2      \
  3*y    3*x     |3*y    3*x|
- ---- - --- + z*|---- + ---|
   2      4      \ 2      4 /

$$- \frac{3 x}{4} - \frac{3 y^{2}}{2} + z \left(\frac{3 x}{4} + \frac{3 y^{2}}{2}\right)$$

     2           /   2      \
  3*y    3*x     |3*y    3*x|
- ---- - --- + z*|---- + ---|
   2      4      \ 2      4 /

$$- \frac{3 x}{4} - \frac{3 y^{2}}{2} + z \left(\frac{3 x}{4} + \frac{3 y^{2}}{2}\right)$$

-3*y^2/2 - 3*x/4 + z*(3*y^2/2 + 3*x/4)

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

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Integral of (3(x+2y^2))/4 dz

Limits of integration:

The graph:

Piecewise:

The solution