Mister Exam

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How to use it?
Integral of d{x}:
Integral of e^3
Integral of 4*x*exp(x^2)
Integral of tan^(-1)x
Integral of x*2^x
Derivative of:
-5x^2
Graphing y =:
-5x^2
Identical expressions
-5x^ two
minus 5x squared
minus 5x to the power of two
-5x2
-5x²
-5x to the power of 2
-5x^2dx
Similar expressions
1/sqrt(2-(5x)^2)
x/(8-5*x^2)
(sqrt5(6-5x^2))
5x^2

Solving integrals/ -5x^2

Integral of -5x^2 dx

The solution

You have entered [src]

  1         
  /         
 |          
 |      2   
 |  -5*x  dx
 |          
/           
0

$$\int\limits_{0}^{1} \left(- 5 x^{2}\right)\, dx$$

Integral(-5*x^2, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- 5 x^{2}\right)\, dx = - 5 \int x^{2}\, dx$
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: $- \frac{5 x^{3}}{3}$
Add the constant of integration:

$- \frac{5 x^{3}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{5 x^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
 |                   3
 |     2          5*x 
 | -5*x  dx = C - ----
 |                 3  
/

$$\int \left(- 5 x^{2}\right)\, dx = C - \frac{5 x^{3}}{3}$$

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.