Surface Area of revolution about the y-axis of x^2]4 - lnx2

In this video, I showed how to compute the surface area of revolution of a function about the y-axis. i explained how to choose the radius of revolution depending on what axis the revolution is about.

[@Samir-zb3xk]

I feel like the question should include the fact that the base of the solid is also bounded by the y-axis, since that is how you drew it but it's not obvious that thats the case from only the initial information given; perhaps something like "The base of a solid is given by the region bounded by the y-axis and the graph y = x²/4 - ln(x)/2 on the interval x∈[1,2]. This region is then rotated about the y-axis to form the solid. Determine the surface area of this solid." Regardless, awesome question and great explanation

[@surendrakverma555]

Thanks Sir for the excellent explanation.

[@RobG1729]

Wouldn't the shape formed by rotation be more like a curved collar instead of a bowl?

[@PrimeNewtons]

Yes a folded collar. The base is not counted. Bowl was the wrong word.

[@RobG1729]

My father was an industrial patternmaker, and blueprints with multiple views were all around his shop. I learned 3D visualization at a young age.

[@ThenSaidHeUntoThem]

Lol 😂 We know all the x' s are greater than 1 for this problem. So, positive.

[@matheodaniloalvitreslopez3159]

This question is to be answered until 11:59 am, for those who have the last digit of their DNI 5: What is the letter you like the most among A, B, C, I, N , The m?

[@anisa7979]

Hi sir one question why ds is square root of 1+f'(x)? is it the same for all the problem?If you have video about it i will make sure to watch ❤

[@Samir-zb3xk]

In general, dS=sqrt((dx)²+(dy)²) because of Pythagoras' theorem. You can factor out a differential depending on what is needed for the problem. In this case he factored out a dx since the expression is in terms of x and the bounds are also x values. so we get dS=sqrt(1+(dy/dx)²)dx; or in Lagrange's notation: dS=sqrt(1+(f'(x))²)dx In a different question we may need the differential dy, or even dt or dθ for parametrically defined functions. So we can manipulate dS=sqrt((dx)²+(dy)²) as neccessary in those situations.

[@anisa7979]

I got it.Thank you so much I am deeply grateful thank you🙏@@Samir-zb3xk

[@matheodaniloalvitreslopez3159]

Esta pregunta es para que me respondan hasta las 11:59 am, para los que tienen el último dígito de su DNI 5 : ¿Cuál es la letra que les gusta más entre la A, la B, la C, la I, la N, la M?

[@Harrykesh630]

professor bring some tough problem these are too easy

[@swadhindas2208]

10:00 sqrt(x^2) = |x| not x

[@jumpman8282]

That's correct, but 𝑥 ∈ [1, 2] ⇒ (𝑥² + 1) ∕ (2𝑥) > 0, which means we can ignore the absolute value.