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Solving integrals/ x^2+5x-14

Integral of x^2+5x-14 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 27                   
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 10                   
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 |  / 2           \   
 |  \x  + 5*x - 14/ dx
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23                    
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10
∫23102710((x2+5x)−14) dx\int\limits_{\frac{23}{10}}^{\frac{27}{10}} \left(\left(x^{2} + 5 x\right) - 14\right)\, dx 
Integral(x^2 + 5*x - 14, (x, 23/10, 27/10))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

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

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

        ∫5x dx=5∫x dx\int 5 x\, dx = 5 \int x\, dx

        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: 5x22\frac{5 x^{2}}{2}

      The result is: x33+5x22\frac{x^{3}}{3} + \frac{5 x^{2}}{2}

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

      ∫(−14) dx=−14x\int \left(-14\right)\, dx = - 14 x

    The result is: x33+5x22−14x\frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 14 x

  2. Now simplify:

    x(2x2+15x−84)6\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}

  3. Add the constant of integration:

    x(2x2+15x−84)6+constant\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2+15x−84)6+constant\frac{x \left(2 x^{2} + 15 x - 84\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                         
 |                                  3      2
 | / 2           \                 x    5*x 
 | \x  + 5*x - 14/ dx = C - 14*x + -- + ----
 |                                 3     2  
/
∫((x2+5x)−14) dx=C+x33+5x22−14x\int \left(\left(x^{2} + 5 x\right) - 14\right)\, dx = C + \frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 14 x
Simplify
The graph
2.702.302.352.402.452.502.552.602.65-2525
Plot the graph f(x)
The answer [src] 
1429
----
750
1429750\frac{1429}{750} 
=
= 
1429
----
750
1429750\frac{1429}{750} 
1429/750
Numerical answer [src] 
1.90533333333334
1.90533333333334

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

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