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Solving integrals/ x/2+1

Integral of x/2+1 dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
 pi           
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0
∫0π(x2+1) dx\int\limits_{0}^{\pi} \left(\frac{x}{2} + 1\right)\, dx 
Integral(x/2 + 1, (x, 0, pi))
Detail solution

  1. Integrate term-by-term:

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

      ∫x2 dx=∫x dx2\int \frac{x}{2}\, dx = \frac{\int x\, dx}{2}

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: x24\frac{x^{2}}{4}

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 dx=x\int 1\, dx = x

    The result is: x24+x\frac{x^{2}}{4} + x

  2. Now simplify:

    x(x+4)4\frac{x \left(x + 4\right)}{4}

  3. Add the constant of integration:

    x(x+4)4+constant\frac{x \left(x + 4\right)}{4}+ \mathrm{constant}

The answer is:

x(x+4)4+constant\frac{x \left(x + 4\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
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 | /x    \              x 
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 | \2    /              4 
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/
∫(x2+1) dx=C+x24+x\int \left(\frac{x}{2} + 1\right)\, dx = C + \frac{x^{2}}{4} + x
Simplify
The graph
0.000.250.500.751.001.251.501.752.002.252.502.753.00010
Plot the graph f(x)
The answer [src] 
       2
     pi 
pi + ---
      4
π24+π\frac{\pi^{2}}{4} + \pi 
=
= 
       2
     pi 
pi + ---
      4
π24+π\frac{\pi^{2}}{4} + \pi 
pi + pi^2/4
Numerical answer [src] 
5.60899375386213
5.60899375386213

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

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