Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2
Integral of x*y
Integral of 8dx
Integral of sqrt(sinx)
Sum of series:
x*y
x*y
Limit of the function:
x*y
Identical expressions
x*y
x multiply by y
xy
x*ydx
Similar expressions
10xy
xye^((x^2)y)

Solving integrals/ x*y

Integral of x*y dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} x y\, dx$$

Integral(x*y, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                2
 |              y*x 
 | x*y dx = C + ----
 |               2  
/

$${{x^2\,y}\over{2}}$$

Simplify

The answer [src]

y
-
2

$${{y}\over{2}}$$

=

y
-
2

$$\frac{y}{2}$$

Упростить

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