What is the surface area of the solid created by revolving #f(x) = x^2-x , x in [2,7]# around the x axis?

Answer 1

See the answer below:

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 ( f(x) = x^2 - x ) around the x-axis over the interval ( x \in [2, 7] ), you can use the formula for the surface area of a solid of revolution:

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

Where ( a = 2 ) and ( b = 7 ), and ( f(x) = x^2 - x ).

First, find ( \frac{df}{dx} ):

[ \frac{df}{dx} = \frac{d}{dx} (x^2 - x) = 2x - 1 ]

Now, plug the function and its derivative into the formula:

[ A = 2\pi \int_{2}^{7} (x^2 - x) \sqrt{1 + (2x - 1)^2} , dx ]

[ = 2\pi \int_{2}^{7} (x^2 - x) \sqrt{1 + 4x^2 - 4x + 1} , dx ]

[ = 2\pi \int_{2}^{7} (x^2 - x) \sqrt{4x^2 - 4x + 2} , dx ]

This integral may require techniques like substitution or other advanced methods to solve, as it involves a square root. Once you find the antiderivative and evaluate it over the interval ([2, 7]), you will have the surface area of the solid of revolution.

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 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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve 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