Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*sin(x)^2
Integral of (x^4+x^(-4)+2)/x^3
Integral of (x-4)/(x-2)(x^2+1)
Integral of x^4-2x^2+4x+1/x^3-x^2-x+1
Canonical form:
-x^2+3x+10
Identical expressions
-x^ two +3x+ ten
minus x squared plus 3x plus 10
minus x to the power of two plus 3x plus ten
-x2+3x+10
-x²+3x+10
-x to the power of 2+3x+10
-x^2+3x+10dx
Similar expressions
-x^2+3x-10
x^2+3x+10
-x^2-3x+10

Integral of -x^2+3x+10 dx

The solution

You have entered [src]

  5                     
  /                     
 |                      
 |  /   2           \   
 |  \- x  + 3*x + 10/ dx
 |                      
/                       
-2

$$\int\limits_{-2}^{5} \left(\left(- x^{2} + 3 x\right) + 10\right)\, dx$$

Integral(-x^2 + 3*x + 10, (x, -2, 5))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
    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: $- \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    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: $\frac{3 x^{2}}{2}$
  The result is: $- \frac{x^{3}}{3} + \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 10\, dx = 10 x$
The result is: $- \frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 10 x$
Now simplify:

$\frac{x \left(- 2 x^{2} + 9 x + 60\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} + 9 x + 60\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} + 9 x + 60\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                    3      2
 | /   2           \                 x    3*x 
 | \- x  + 3*x + 10/ dx = C + 10*x - -- + ----
 |                                   3     2  
/

$$\int \left(\left(- x^{2} + 3 x\right) + 10\right)\, dx = C - \frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

343/6

$$\frac{343}{6}$$

343/6

$$\frac{343}{6}$$

343/6

Numerical answer [src]

57.1666666666667

57.1666666666667

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of -x^2+3x+10 dx

Limits of integration:

The graph:

Piecewise:

The solution