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Mathematics

2 answers:

kari74 [83]3 years ago

5 0

Answer:

LORD HAVE MERCY

Step-by-step explanation:

SLIDE EM POINTS AND TX

djverab [1.8K]3 years ago

5 0

Thank you so much for these free points

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prohojiy [21]

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3 years ago

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y=√x and y=x^2. Find V either by sl

Ede4ka [16]

Answer:

The volume of the solid is $3\pi/10$

Step-by-step explanation:

In this case, the washer method seems to be easier and thus, it is the one I will use.

Since the rotation is around the y-axis we need to change de dependency of our variables to have $f(x)\rightarrow f(y)$ . Thus, our functions with $y$ as independent variable are:

$x=\sqrt{y}\\ x=y^2$

For the washer method, we need to find the area function, which is given by:

$A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]$

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function $x=\sqrt{y}$ and the inner one by $x=y^2$ . Thus, the area function is:

$A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)$

Now we just need to integrate. The integration limits are easy to find by just solving the equation $\sqrt(y)=y^2$ , which has two solutions $y=0$ and $y=1$ . These are then, our integration limits.