Mister Exam

Integral of 24+x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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01(x+24)dx\int\limits_{0}^{1} \left(x + 24\right)\, dx
Integral(24 + x, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

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

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

      24dx=24x\int 24\, dx = 24 x

    The result is: x22+24x\frac{x^{2}}{2} + 24 x

  2. Now simplify:

    x(x+48)2\frac{x \left(x + 48\right)}{2}

  3. Add the constant of integration:

    x(x+48)2+constant\frac{x \left(x + 48\right)}{2}+ \mathrm{constant}


The answer is:

x(x+48)2+constant\frac{x \left(x + 48\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                   2       
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 | (24 + x) dx = C + -- + 24*x
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(x+24)dx=C+x22+24x\int \left(x + 24\right)\, dx = C + \frac{x^{2}}{2} + 24 x
The graph
0.001.000.100.200.300.400.500.600.700.800.90050
The answer [src]
49/2
492\frac{49}{2}
=
=
49/2
492\frac{49}{2}
49/2
Numerical answer [src]
24.5
24.5

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