Mister Exam

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Integral of d{x}:
Integral of y=kx^2
Integral of e^(5x)×sin3x
Integral of 9dx
Integral of ctg(2x)
Identical expressions
y=kx^ two
y equally kx squared
y equally kx to the power of two
y=kx2
y=kx²
y=kx to the power of 2
y=kx^2dx

Solving integrals/ y=kx^2

Integral of y=kx^2 dx

The solution

You have entered [src]

$$\int\limits_{4}^{1} k x^{2}\, dx$$

Integral(k*x^2, (x, 4, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{k\,x^3}\over{3}}$$

Simplify

The answer [src]

-21*k

$$-21\,k$$

=

-21*k

$$- 21 k$$

Simplify

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