Mister Exam

Lang:

Solving integrals/ y=4-x

Integral of y=4-x dx

You have entered [src]

  1           
  /           
 |            
 |  (4 - x) dx
 |            
/             
0

$$\int\limits_{0}^{1} \left(4 - x\right)\, dx$$

Integral(4 - x, (x, 0, 1))

Detail solution

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

$\frac{x \left(8 - x\right)}{2}$
Add the constant of integration:

$\frac{x \left(8 - x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(8 - x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        2
 |                        x 
 | (4 - x) dx = C + 4*x - --
 |                        2 
/

$$4\,x-{{x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/2

$${{7}\over{2}}$$

7/2

$$\frac{7}{2}$$

Упростить

Numerical answer [src]

3.5

3.5

The graph

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