# What is the surface area of the solid created by revolving #f(x)=x^2# for #x in [1,2]# around the x-axis?

Now, integrating by parts

=

=

=

Now transposing

Thus

Like wise, using technique of integration by parts

=

=

Now transpose

Now using the integral of

=

Now substituting theta by x it would be

The required surface area would thus be

=

```
*****
```

`Sign up to view the whole answer`

`By signing up, you agree to our Terms of Service and Privacy Policy`

`Sign up with email`

`Answer 2`To find the surface area of the solid created by revolving the function ( f(x) = x^2 ) for ( x ) in the interval ([1,2]) around the x-axis, you can use the formula for the surface area of a solid of revolution:

[ S = 2\pi \int_{1}^{2} f(x) \sqrt{1 + \left(\frac{df}{dx}\right)^2} , dx ]

Where ( \frac{df}{dx} ) represents the derivative of ( f(x) ) with respect to ( x ). In this case, ( f(x) = x^2 ), so ( \frac{df}{dx} = 2x ).

Substituting the values into the formula:

[ S = 2\pi \int_{1}^{2} x^2 \sqrt{1 + (2x)^2} , dx ]

Now, you can integrate this expression within the given bounds to find the surface area of the solid.

Sign up to view the whole answerBy signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

`Answer 3`To find the surface area of the solid created by revolving the function ( f(x) = x^2 ) for ( x ) in the interval ([1,2]) around the x-axis, you can use the formula for the surface area of a solid of revolution, which is given by:

[ S = 2\pi \int_{a}^{b} f(x) \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx ]

where ( f(x) ) is the function being rotated, and ( a ) and ( b ) are the limits of integration.

In this case, ( f(x) = x^2 ), ( a = 1 ), and ( b = 2 ). The derivative of ( f(x) ) is ( f'(x) = 2x ). Plugging these into the formula:

[ S = 2\pi \int_{1}^{2} x^2 \sqrt{1 + (2x)^2} dx ]

You can evaluate this integral to find the surface area.

Sign up to view the whole answerBy signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

`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.`

`Trending questions`

`How do you determine if #f(x,y)=-x^3-4xy^2+y^3# is homogeneous and what would it's degree be?`

`What is the first derivative of the curve described by #y = 1/2root(3)(x) + 8/x + 1#?`

`How do you find the length of the curve #y=e^x# between #0<=x<=1# ?`

`How do you find the point c in the interval #0<=x<=2# such that f(c) is equation to the average value of #f(x)=x^(2/3)#?`

`What is a solution to the differential equation #dy/dx=xe^y#?`

`Not the question you need? `

`HIX TutorSolve ANY homework problem with a smart AI`- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7