Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*e^(x*(-2))
Integral of 1/(2+3x^2)
Integral of x(x+1)^1/2
Integral of (x^3-1)^1/2
Identical expressions
nine /50x- three /100x^ two
9 divide by 50x minus 3 divide by 100x squared
nine divide by 50x minus three divide by 100x to the power of two
9/50x-3/100x2
9/50x-3/100x²
9/50x-3/100x to the power of 2
9 divide by 50x-3 divide by 100x^2
9/50x-3/100x^2dx
Similar expressions
9/50x+3/100x^2

Integral of 9/50x-3/100x^2 dx

The solution

You have entered [src]

  6                
  /                
 |                 
 |  /         2\   
 |  |9*x   3*x |   
 |  |--- - ----| dx
 |  \ 50   100 /   
 |                 
/                  
0

$$\int\limits_{0}^{6} \left(- \frac{3 x^{2}}{100} + \frac{9 x}{50}\right)\, dx$$

Integral(9*x/50 - 3*x^2/100, (x, 0, 6))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{3 x^{2}}{100}\right)\, dx = - \frac{3 \int x^{2}\, dx}{100}$
  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: $- \frac{x^{3}}{100}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{9 x}{50}\, dx = \frac{9 \int x\, dx}{50}$
  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: $\frac{9 x^{2}}{100}$
The result is: $- \frac{x^{3}}{100} + \frac{9 x^{2}}{100}$
Now simplify:

$\frac{x^{2} \left(9 - x\right)}{100}$
Add the constant of integration:

$\frac{x^{2} \left(9 - x\right)}{100}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(9 - x\right)}{100}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                 
 | /         2\            3      2
 | |9*x   3*x |           x    9*x 
 | |--- - ----| dx = C - --- + ----
 | \ 50   100 /          100   100 
 |                                 
/

$$\int \left(- \frac{3 x^{2}}{100} + \frac{9 x}{50}\right)\, dx = C - \frac{x^{3}}{100} + \frac{9 x^{2}}{100}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

27
--
25

$$\frac{27}{25}$$

27
--
25

$$\frac{27}{25}$$

27/25

Numerical answer [src]

1.08

1.08

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 9/50x-3/100x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution