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Solving integrals/ (-1)/sqrt(y)

Integral of (-1)/sqrt(y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
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0
∫01(−1y) dy\int\limits_{0}^{1} \left(- \frac{1}{\sqrt{y}}\right)\, dy 
Integral(-1/sqrt(y), (y, 0, 1))
Detail solution

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

    ∫(−1y) dy=−∫1y dy\int \left(- \frac{1}{\sqrt{y}}\right)\, dy = - \int \frac{1}{\sqrt{y}}\, dy

    1. Let u=yu = \sqrt{y}.

      Then let du=dy2ydu = \frac{dy}{2 \sqrt{y}} and substitute 2du2 du:

      ∫2 du\int 2\, du

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

        False\text{False}

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

          ∫1 du=u\int 1\, du = u

        So, the result is: 2u2 u

      Now substitute uu back in:

      2y2 \sqrt{y}

    So, the result is: −2y- 2 \sqrt{y}

  2. Add the constant of integration:

    −2y+constant- 2 \sqrt{y}+ \mathrm{constant}

The answer is:

−2y+constant- 2 \sqrt{y}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
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 | ----- dy = C - 2*\/ y 
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∫(−1y) dy=C−2y\int \left(- \frac{1}{\sqrt{y}}\right)\, dy = C - 2 \sqrt{y}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-100100
Plot the graph f(x)
The answer [src] 
-2
−2-2 
=
= 
-2
−2-2 
-2
Numerical answer [src] 
-1.99999999946942
-1.99999999946942

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

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