Mister Exam

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Integral of 4t-t^2
Graphing y =:
4t-t^2
Identical expressions
4t-t^ two
4t minus t squared
4t minus t to the power of two
4t-t2
4t-t²
4t-t to the power of 2
Similar expressions
4t+t^2

Integral of 4t-t^2 dx

The solution

You have entered [src]

  1              
  /              
 |               
 |  /       2\   
 |  \4*t - t / dt
 |               
/                
0

$$\int\limits_{0}^{1} \left(- t^{2} + 4 t\right)\, dt$$

Integral(4*t - t^2, (t, 0, 1))

Detail solution

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

$\frac{t^{2} \left(6 - t\right)}{3}$
Add the constant of integration:

$\frac{t^{2} \left(6 - t\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{t^{2} \left(6 - t\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                             3
 | /       2\             2   t 
 | \4*t - t / dt = C + 2*t  - --
 |                            3 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$$\frac{5}{3}$$

5/3

$$\frac{5}{3}$$

5/3

Numerical answer [src]

1.66666666666667

1.66666666666667

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

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Identical expressions

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Integral of 4t-t^2 dx

Limits of integration:

The graph:

Piecewise:

The solution