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    I THINK this is a question on volume of revolution but im not sure but if it is then how do do i square this?

    y= 3x+1/√x to give y2=.....

    The question is the diagram shows the curve with equation
    y= 3x+1/√x, x>0.

    The shaded region is bounded by the curve, the x-axis and the lines x=1 and x=3.

    Find the volume of the solid formed when the shaded region is rotated through 4 right angles about the x-axis, giving your answer in the form
    π(a + ln b) where a and b are integers.

    Another question is if it is Volumes of Revolution, where does ln come from in the answer?
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    (Original post by ZarqaaX)
    I THINK this is a question on volume of revolution but im not sure but if it is then how do do i square this?

    y= 3x+1/√x to give y2=.....

    The question is the diagram shows the curve with equation
    y= 3x+1/√x, x>0.

    The shaded region is bounded by the curve, the x-axis and the lines x=1 and x=3.

    Find the volume of the solid formed when the shaded region is rotated through 4 right angles about the x-axis, giving your answer in the form
    π(a + ln b) where a and b are integers.

    Another question is if it is Volumes of Revolution, where does ln come from in the answer?
    To find the volume of the solid formed from the revolution of the curve around the x-axis, you must use the formula :

    V = \displaystyle \pi \int_{x=a}^{x=b} y^2\ dx

    Once you find y^2 you'll soon come to realise why the natural logarithmic term is there.
    Hint
    \displaystyle \int \dfrac{1}{x}\ dx = \ln |x| + C
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    definitely volume of revolution.

    integrate πy2dx

    part of the expression will be a/x which when integrated will be aln|x|
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    (Original post by the bear)
    definitely volume of revolution.

    integrate πy2dx

    part of the expression will be a/x which when integrated will be aln|x|
    I dont know how to square y to give y2 :/

    y = 3x+1 / √x, it looks weird so im finding it hard to square lool
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    (Original post by ZarqaaX)
    I dont know how to square y to give y2 :/

    y = 3x+1 / √x, it looks weird so im finding it hard to square lool
    Hint:

    (a+b)^2 = (a+b)(a+b) = a^2 + 2ab + b^2

    So can you fill the following in now?

    \displaystyle \left(3x + \frac{1}{\sqrt{x}}\right)^2 = ...
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    (Original post by ZarqaaX)
    I dont know how to square y to give y2 :/

    y = 3x+1 / √x, it looks weird so im finding it hard to square lool
    How do you not know how to expand the product of two parentheses when you're doing A2 integration?

    I suspect that you want us to do it for you, but we won't.
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    (Original post by Indeterminate)
    Hint:

    (a+b)^2 = (a+b)(a+b) = a^2 + 2ab + b^2

    So can you fill the following in now?

    \displaystyle \left(3x + \frac{1}{\sqrt{x}}\right)^2 = ...
    Ahh yes i understand it now, i completely forgot that you can separate them, thank you! I didnt understand it properly as i didnt get the notes since i missed the lesson and i had to catch up pretty fast :/
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    (Original post by Khallil)
    How do you not know how to expand the product of two parentheses when you're doing A2 integration?

    I suspect that you want us to do it for you, but we won't.
    I'm sorry that you think that but i'm not wanting everyone to do it all for me i just wanted help because i was just stuck on some things and integration is pretty hard and i get muddled up with equations sometimes
 
 
 

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