Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of -4/x
Integral of 1/(1+x²)
Integral of 1/(1+x)^2
Integral of 1/1+x
Graphing y =:
(4/3)*x+12
Identical expressions
(four / three)*x+ twelve
(4 divide by 3) multiply by x plus 12
(four divide by three) multiply by x plus twelve
(4/3)x+12
4/3x+12
(4 divide by 3)*x+12
(4/3)*x+12dx
Similar expressions
(4/3)*x-12

Integral of (4/3)*x+12 dx

The solution

You have entered [src]

 12              
  /              
 |               
 |  /4*x     \   
 |  |--- + 12| dx
 |  \ 3      /   
 |               
/                
0

$$\int\limits_{0}^{12} \left(\frac{4 x}{3} + 12\right)\, dx$$

Integral(4*x/3 + 12, (x, 0, 12))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{4 x}{3}\, dx = \frac{4 \int x\, dx}{3}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{2 x^{2}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 12\, dx = 12 x$
The result is: $\frac{2 x^{2}}{3} + 12 x$
Now simplify:

$\frac{2 x \left(x + 18\right)}{3}$
Add the constant of integration:

$\frac{2 x \left(x + 18\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 x \left(x + 18\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                               2
 | /4*x     \                 2*x 
 | |--- + 12| dx = C + 12*x + ----
 | \ 3      /                  3  
 |                                
/

$$\int \left(\frac{4 x}{3} + 12\right)\, dx = C + \frac{2 x^{2}}{3} + 12 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$240$$

Numerical answer [src]

240.0

240.0

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (4/3)*x+12 dx

Limits of integration:

The graph:

Piecewise:

The solution