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Maths integration. Need help!

Here is a link to the problem:
http://postimg.org/image/lj5hd20kj/
I don't know what dy is!
I honestly am so tired and frustrated, I taught myself differentiation in a couple days, but integration has me pulling my hair out.
surely the dy of y^1/2 is
2/3 y ^3/2
because when you differentiate you - 1 from the power, so working in reverse order.
y^1/2+1 = y^3/2
so what times' by 3/2 to make 1? 2/3, surely?
but I keep getting wrong answer?
I'm getting incredibly frustrated. have posted on here 3 times now with no help.
Anyone?
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by Danny.L
Here is a link to the problem:
http://postimg.org/image/lj5hd20kj/
I don't know what dy is!
I honestly am so tired and frustrated, I taught myself differentiation in a couple days, but integration has me pulling my hair out.
surely the dy of y^1/2 is
2/3 y ^3/2
because when you differentiate you - 1 from the power, so working in reverse order.
y^1/2+1 = y^3/2
so what times' by 3/2 to make 1? 2/3, surely?
but I keep getting wrong answer?
I'm getting incredibly frustrated. have posted on here 3 times now with no help.
Anyone?


what board are you doing?
Reply 2
Avatar for Bob2222
Bob2222
1
Original post by Danny.L
Here is a link to the problem:
http://postimg.org/image/lj5hd20kj/
I don't know what dy is!
I honestly am so tired and frustrated, I taught myself differentiation in a couple days, but integration has me pulling my hair out.
surely the dy of y^1/2 is
2/3 y ^3/2
because when you differentiate you - 1 from the power, so working in reverse order.
y^1/2+1 = y^3/2
so what times' by 3/2 to make 1? 2/3, surely?
but I keep getting wrong answer?
I'm getting incredibly frustrated. have posted on here 3 times now with no help.
Anyone?



yes ∫y^(1/2) dy = (2/3)y^(3/2) +c

integration is the opposite of differentiation so just add one to the power then divide by it. But don't forget the constant +c because if you differentiated 3x+2 for example you would get 3... the 2 'disappears' so doing the reverse you write +c on the end to represent the unknown number.
Reply 3
Avatar for davros
davros
16
Original post by Danny.L
Here is a link to the problem:
http://postimg.org/image/lj5hd20kj/
I don't know what dy is!
I honestly am so tired and frustrated, I taught myself differentiation in a couple days, but integration has me pulling my hair out.
surely the dy of y^1/2 is
2/3 y ^3/2
because when you differentiate you - 1 from the power, so working in reverse order.
y^1/2+1 = y^3/2
so what times' by 3/2 to make 1? 2/3, surely?
but I keep getting wrong answer?
I'm getting incredibly frustrated. have posted on here 3 times now with no help.
Anyone?


What answer do you get for the area in the first question?
Reply 4
Avatar for Danny.L
Danny.L
OP
3
Original post by davros
What answer do you get for the area in the first question?

the answer is 36 but I have no idea how to get it!
Reply 5
Avatar for davros
davros
16
Original post by Danny.L
the answer is 36 but I have no idea how to get it!


I must be going a bit mad then, because I get 16/3 for area A and hence 32/3 for the total area.
Reply 6
Avatar for Phichi
Phichi
11
Original post by davros
I must be going a bit mad then, because I get 16/3 for area A and hence 32/3 for the total area.


Original post by Danny.L
the answer is 36 but I have no idea how to get it!


It looks like the answer box is for a mixed fraction, but davros is definitely right.
Original post by buxtonarmy
Area A is 8/3 and hence 16/3 for the total area?


No

I think you might have found the area under the curve
(edited 9 years ago)
Reply 8
Avatar for davros
davros
16
Original post by buxtonarmy
Area A is 8/3 and hence 16/3 for the total area?


A=23×43/2=23×8=163A = \dfrac{2}{3} \times 4^{3/2} = \dfrac{2}{3} \times 8 = \dfrac{16}{3}

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