Mister Exam

Integral of (x+y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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01(x+y)dx\int\limits_{0}^{1} \left(x + y\right)\, dx
Integral(x + y, (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:

      ydx=xy\int y\, dx = x y

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

  2. Now simplify:

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

  3. Add the constant of integration:

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


The answer is:

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

The answer (Indefinite) [src]
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(x+y)dx=C+x22+xy\int \left(x + y\right)\, dx = C + \frac{x^{2}}{2} + x y
The answer [src]
1/2 + y
y+12y + \frac{1}{2}
=
=
1/2 + y
y+12y + \frac{1}{2}
1/2 + y

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