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Solving integrals/ 7*x^2+y

Integral of 7*x^2+y dy

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫02x(7x2+y) dy\int\limits_{0}^{2 \sqrt{x}} \left(7 x^{2} + y\right)\, dy 
Integral(7*x^2 + y, (y, 0, 2*sqrt(x)))
Detail solution

  1. Integrate term-by-term:

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

      ∫7x2 dy=7x2y\int 7 x^{2}\, dy = 7 x^{2} y

    1. The integral of yny^{n} is yn+1n+1\frac{y^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫y dy=y22\int y\, dy = \frac{y^{2}}{2}

    The result is: 7x2y+y227 x^{2} y + \frac{y^{2}}{2}

  2. Now simplify:

    y(14x2+y)2\frac{y \left(14 x^{2} + y\right)}{2}

  3. Add the constant of integration:

    y(14x2+y)2+constant\frac{y \left(14 x^{2} + y\right)}{2}+ \mathrm{constant}

The answer is:

y(14x2+y)2+constant\frac{y \left(14 x^{2} + y\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                      2         
 | /   2    \          y         2
 | \7*x  + y/ dy = C + -- + 7*y*x 
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∫(7x2+y) dy=C+7x2y+y22\int \left(7 x^{2} + y\right)\, dy = C + 7 x^{2} y + \frac{y^{2}}{2}
Simplify
The answer [src] 
          5/2
2*x + 14*x
14x52+2x14 x^{\frac{5}{2}} + 2 x 
=
= 
          5/2
2*x + 14*x
14x52+2x14 x^{\frac{5}{2}} + 2 x 
2*x + 14*x^(5/2)

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

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