Intergration

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kitkat132000
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#1
Report Thread starter 5 years ago
#1
Can someone help me with this question? If u r asked to intergrate something don't u get it in the dy/dx form but here I've been given y= and they want me to intergrate it?

It is given that y=x^1/3
Find ∫y dx
8
Hence evaluate ∫y dx
0

The 8 is meant to be on top of theintergral and the 0 at the bottom.
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Hajra Momoniat
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#2
Report 5 years ago
#2
The equation that you get in the question does not have to be in the form of dy/dx and can be in the form of y or f(x).

Integration: So from the equation x^1/3 you apply the same rules for integration (add one to the power, divide by the new power). So 1/3 add 1 is 4/3 which is your new power and the coefficient in front of the x (being a 1) is divided by 4/3 to give 3/4. So your answer is 3/4x^4/3.

Differentiation: again, apply the same rules for differentiation for x^1/3 (bring down the power take one off the power). So bring down the power by multiplying the 1/3 by the coefficient in front of the x (being the 1) to give 1/3. Then do 1/3 subtract 1 to give -2/3. So your answer is 1/3x^-2/3.

Hopefully this has helped
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kitkat132000
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#3
Report Thread starter 5 years ago
#3
(Original post by Hajra Momoniat)
The equation that you get in the question does not have to be in the form of dy/dx and can be in the form of y or f(x).

Integration: So from the equation x^1/3 you apply the same rules for integration (add one to the power, divide by the new power). So 1/3 add 1 is 4/3 which is your new power and the coefficient in front of the x (being a 1) is divided by 4/3 to give 3/4. So your answer is 3/4x^4/3.

Differentiation: again, apply the same rules for differentiation for x^1/3 (bring down the power take one off the power). So bring down the power by multiplying the 1/3 by the coefficient in front of the x (being the 1) to give 1/3. Then do 1/3 subtract 1 to give -2/3. So your answer is 1/3x^-2/3.

Hopefully this has helped
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I've attached the question above. I know how to intergrate and differentiate but I'm not sure on what the questions asking me to do, is it asking me to intergrate or differentiate? It has the intergral sign but we r given y= and not dy/dx which left me confused
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Hajra Momoniat
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#4
Report 5 years ago
#4
Apply the same integration in my first reply to (i)

For (ii) you need to use the formula called "the trapezium rule". This is

[img]data:image/png;base64,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[/img]

and then substitute the numbers
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Hajra Momoniat
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#5
Report 5 years ago
#5
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[/img]



sorry all the garbage is meant to be the trapezium rule which is the above XD
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Hajra Momoniat
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#6
Report 5 years ago
#6
I give up with inserting the image. so sorry
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