Integral of 3x³-4x² dx

The solution

You have entered [src]

  4                 
  /                 
 |                  
 |  /   3      2\   
 |  \3*x  - 4*x / dx
 |                  
/                   
2

$$\int\limits_{2}^{4} \left(3 x^{3} - 4 x^{2}\right)\, dx$$

Integral(3*x^3 - 4*x^2, (x, 2, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{3}\, dx = 3 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $\frac{3 x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x^{2}\right)\, dx = - 4 \int x^{2}\, dx$
  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: $- \frac{4 x^{3}}{3}$
The result is: $\frac{3 x^{4}}{4} - \frac{4 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(9 x - 16\right)}{12}$
Add the constant of integration:

$\frac{x^{3} \left(9 x - 16\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(9 x - 16\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                           3      4
 | /   3      2\          4*x    3*x 
 | \3*x  - 4*x / dx = C - ---- + ----
 |                         3      4  
/

$$\int \left(3 x^{3} - 4 x^{2}\right)\, dx = C + \frac{3 x^{4}}{4} - \frac{4 x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

316/3

$$\frac{316}{3}$$

316/3

$$\frac{316}{3}$$

316/3

Numerical answer [src]

105.333333333333

105.333333333333

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 3x³-4x² dx

Limits of integration:

The graph:

Piecewise:

The solution