Y=sqrt(x), y=0, x=0,and x=2 a. Find the area of the region b. find the volume of the solid formed by rotating the region about the x-axis c. find the volume of the solid?

Answer 1

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a)

#A=int_0^2sqrtx*dx#

#A=[x^(3/2)]_0^2=sqrt8 #

b)

#volume=int_0^2pi*y^2*dx#

#volume=int_0^2pi*x*dx=1/2pi[x^2]_0^2=2pi#

c)This command doesnot complete

this is the sketch of the function.

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Answer 2

a. The area of the region is given by the integral of ( y = \sqrt{x} ) from ( x = 0 ) to ( x = 2 ): [ \text{Area} = \int_{0}^{2} \sqrt{x} , dx ]

b. To find the volume of the solid formed by rotating the region about the x-axis, we use the method of cylindrical shells. The volume is given by the integral: [ V = 2\pi \int_{0}^{2} x \sqrt{x} , dx ]

c. To find the volume of the solid formed by rotating the region about the y-axis, we need to use the washer method. The volume is given by the integral: [ V = \pi \int_{0}^{2} (\sqrt{x})^2 , dx ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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