# Intergration

#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.
0
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
0
#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

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
0
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

and then substitute the numbers
0
5 years ago
#5

sorry all the garbage is meant to be the trapezium rule which is the above XD
0
5 years ago
#6
I give up with inserting the image. so sorry
0
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