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Integration- Area between 2 lines

Hi there, i need some help on this integration question. I only need some help on what to do first as im pretty sure i could then carry on but im not sure where to start first.

Find the area of the region bounded by parts of the y axis, the curve y=x^3 and the lines y=1 and y=27.

Thanks. If someone could tell me what to write and calculate for the first couple of steps that would be awesome.
Reply 1
Avatar for TheDavibob
TheDavibob
First of all, sketch out the graph, it'll help you figure out which areas precisely you need.

Now, what area would calculating ∫13x3dx\int_{1}^{3} x^3 dx give you?

How can you calculate the area you actually want from this?

I don't know whether this post is particularly clear - sketch the graph and see if you can understand what I'm saying.
Reply 2
Avatar for nuodai
nuodai
17
Original post by TheDavibob
First of all, sketch out the graph, it'll help you figure out which areas precisely you need.

Now, what area would calculating ∫13x3dx\int_{1}^{3} x^3 dx give you?

How can you calculate the area you actually want from this?

I don't know whether this post is particularly clear - sketch the graph and see if you can understand what I'm saying.


That finds the area between the graph, the lines x=1 and x=3, and the x-axis; however, this question asks for the area between the graph, the lines y=1 and y=3, and the y-axis.

In this case you need to write the equation in the form x=f(y)x=f(y) (so that we're basically switching the axes, but changing the function to match). Then you can integrate between the appropriate limits.
Reply 3
Avatar for Femto
Femto
8
Original post by ~Sparked~
Hi there, i need some help on this integration question. I only need some help on what to do first as im pretty sure i could then carry on but im not sure where to start first.

Find the area of the region bounded by parts of the y axis, the curve y=x^3 and the lines y=1 and y=27.

Thanks. If someone could tell me what to write and calculate for the first couple of steps that would be awesome.


Think about how you'd tackle it between the y axis.

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