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)
Identical expressions
three √(three -7x)
3√(3 minus 7x)
three √(three minus 7x)
3√3-7x
3√(3-7x)dx
Similar expressions
3√(3+7x)

Integral of 3√(3-7x) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |      _________   
 |  3*\/ 3 - 7*x  dx
 |                  
/                   
0

$$\int\limits_{0}^{1} 3 \sqrt{3 - 7 x}\, dx$$

Integral(3*sqrt(3 - 7*x), (x, 0, 1))

Detail solution

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

$\int 3 \sqrt{3 - 7 x}\, dx = 3 \int \sqrt{3 - 7 x}\, dx$
1. Let $u = 3 - 7 x$ .
  
  Then let $du = - 7 dx$ and substitute $- \frac{du}{7}$ :
  
  $\int \left(- \frac{\sqrt{u}}{7}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \sqrt{u}\, du = - \frac{\int \sqrt{u}\, du}{7}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
    So, the result is: $- \frac{2 u^{\frac{3}{2}}}{21}$
  Now substitute $u$ back in:
  
  $- \frac{2 \left(3 - 7 x\right)^{\frac{3}{2}}}{21}$
So, the result is: $- \frac{2 \left(3 - 7 x\right)^{\frac{3}{2}}}{7}$
Add the constant of integration:

$- \frac{2 \left(3 - 7 x\right)^{\frac{3}{2}}}{7}+ \mathrm{constant}$

The answer is:

$- \frac{2 \left(3 - 7 x\right)^{\frac{3}{2}}}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                   3/2
 |     _________          2*(3 - 7*x)   
 | 3*\/ 3 - 7*x  dx = C - --------------
 |                              7       
/

$$\int 3 \sqrt{3 - 7 x}\, dx = C - \frac{2 \left(3 - 7 x\right)^{\frac{3}{2}}}{7}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___       
6*\/ 3    16*I
------- + ----
   7       7

$$\frac{6 \sqrt{3}}{7} + \frac{16 i}{7}$$

    ___       
6*\/ 3    16*I
------- + ----
   7       7

$$\frac{6 \sqrt{3}}{7} + \frac{16 i}{7}$$

6*sqrt(3)/7 + 16*i/7

Numerical answer [src]

(1.4852659072284 + 2.28458266370697j)

(1.4852659072284 + 2.28458266370697j)

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 3√(3-7x) dx

Limits of integration:

The graph:

Piecewise:

The solution