Mister Exam

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How to use it?
Integral of d{x}:
Integral of a
Integral of e^2x
Integral of -1/t
Integral of x/y
Derivative of:
ax^2
Identical expressions
ax^ two
ax squared
ax to the power of two
ax2
ax²
ax to the power of 2
ax^2dx
Similar expressions
(-a)/((sqrt(1-acos(a*x)^2)*sqrt(1-a^2*x^2)))

Solving integrals/ ax^2

Integral of ax^2 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} a x^{2}\, dx$$

Integral(a*x^2, (x, 0, 1))

Detail solution

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

$\int a x^{2}\, dx = a \int x^{2}\, dx$
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: $\frac{a x^{3}}{3}$
Add the constant of integration:

$\frac{a x^{3}}{3}+ \mathrm{constant}$

The answer is:

$\frac{a x^{3}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                  3
 |    2          a*x 
 | a*x  dx = C + ----
 |                3  
/

$$\int a x^{2}\, dx = C + \frac{a x^{3}}{3}$$

Simplify

The answer [src]

a
-
3

$$\frac{a}{3}$$

=

a
-
3

$$\frac{a}{3}$$

a/3

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