Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(x^2)
Integral of sin(x)^3
Integral of √(x^2+1)
Integral of cos(5x)
Graphing y =:
sqrt(2)*x
Identical expressions
sqrt(two)*x
square root of (2) multiply by x
square root of (two) multiply by x
√(2)*x
sqrt(2)x
sqrt2x
sqrt(2)*xdx
Similar expressions
1dx/(x^2sqrt2x-4)
1-root3(2x)/sqrt(2x)
x/sqrt(2*x^2+2*x+3)
d×x/(2x-sqrt2x)
(sqrt(2x)+x^(3/2))

Solving integrals/ sqrt(2)*x

Integral of sqrt(2)*x dx

The solution

You have entered [src]

  2           
  /           
 |            
 |    ___     
 |  \/ 2 *x dx
 |            
/             
-6

$$\int\limits_{-6}^{2} \sqrt{2} x\, dx$$

Integral(sqrt(2)*x, (x, -6, 2))

Detail solution

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

$\int \sqrt{2} x\, dx = \sqrt{2} \int x\, dx$
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: $\frac{\sqrt{2} x^{2}}{2}$
Add the constant of integration:

$\frac{\sqrt{2} x^{2}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{2} x^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                    ___  2
 |   ___            \/ 2 *x 
 | \/ 2 *x dx = C + --------
 |                     2    
/

$$\int \sqrt{2} x\, dx = C + \frac{\sqrt{2} x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      ___
-16*\/ 2

$$- 16 \sqrt{2}$$

=

      ___
-16*\/ 2

$$- 16 \sqrt{2}$$

-16*sqrt(2)

Numerical answer [src]

-22.6274169979695

-22.6274169979695

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