Integral of 2sqrt(x) dx

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

Integral(2*sqrt(x), (x, 0, 1))

Detail solution

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

$\int 2 \sqrt{x}\, dx = 2 \int \sqrt{x}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
So, the result is: $\frac{4 x^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{4 x^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

\frac{4 x^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]

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\int 2 \sqrt{x}\, dx = C + \frac{4 x^{\frac{3}{2}}}{3}

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

\frac{4}{3}

4/3

\frac{4}{3}

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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