C2: Finding area of a curve

ckfeister

a) Find the area between the y-axis, and the curves y = x² and y = 2 + √2√x, given that the curves intersect at (2,4)

Here is my workings out but it says the answer is 4 sq. units... what have I done wrong along the way?

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Reply 1

Muttley79

Original post by ckfeister

a) Find the area between the y-axis, and the curves y = x² and y = 2 + √2√x, given that the curves intersect at (2,4)

Here is my workings out but it says the answer is 4 sq. units... what have I done wrong along the way?

Check your second integration - the integral of 2 is not 2 and the second term is also incorrect.

(edited 7 years ago)

Reply 2

ckfeister

Original post by Muttley79

Check your second integration - the integral of 2 is not 2 and the second term is also incorrect.

Its 2x and got 9 1/3 sq. unit now.... what am I doing wrong? The answer is 4.

Reply 3

ckfeister

Original post by Muttley79

Check your second integration - the integral of 2 is not 2 and the second term is also incorrect.

Ohh forgot to do the bottom part, I got 68/9 for second part, but got 44/9 sq.unit now (4.8888...) what else have I done wrong?

Reply 4

Muttley79

Original post by ckfeister

Ohh forgot to do the bottom part, I got 68/9 for second part, but got 44/9 sq.unit now (4.8888...) what else have I done wrong?

They want the area between the curcve and the Y AXIS ... what are you finding?

Reply 5

Notnek

Original post by ckfeister

Ohh forgot to do the bottom part, I got 68/9 for second part, but got 44/9 sq.unit now (4.8888...) what else have I done wrong?

You should be getting 20/3 for your second integral.

Have another go and please post your working if you don't get it.

Reply 6

ckfeister

Original post by Muttley79

They want the area between the curcve and the Y AXIS ... what are you finding?

I got the integral wrong I forgot you add one power and divide by the new power. I'm using x = 2 x = 0 as the area finder.

Reply 7

ckfeister

Original post by notnek

You should be getting 20/3 for your second integral.

Have another go and please post your working if you don't get it.

I can't see how I can improve from this... can you hint it out?

Reply 8

Muttley79

Original post by ckfeister

I can't see how I can improve from this... can you hint it out?

Check what you are doing - I can't see that you are finding the right area - where are you dealing with the y-axis?

Reply 9

ckfeister

Original post by Muttley79

Check what you are doing - I can't see that you are finding the right area - where are you dealing with the y-axis?

(2,4) is the intersecting points, so I'm using 2,0, this is the area for area B (one thats wrong) I don't see how it 20/3 but somehow it is.

Reply 10

Muttley79

Original post by ckfeister

(2,4) is the intersecting points, so I'm using 2,0, this is the area for area B (one thats wrong) I don't see how it 20/3 but somehow it is.

The area should be integrated with respect to y shouldn't it...

Reply 11

Notnek

Original post by ckfeister

I can't see how I can improve from this... can you hint it out?

Your problem is with the integral of

2^\frac{1}{2}x^\frac{1}{2}

Remember that

2^\frac{1}{2}

is just a number like

2

so hink about how you integrate

2x^\frac{1}{2}

and do a similar thing here.

Reply 12

Notnek

Original post by ckfeister

a) Find the area between the y-axis, and the curves y = x² and y = 2 + √2√x, given that the curves intersect at (2,4)

I just noticed that the question includes the y-axis, as Muttley has pointed out.

Are you sure you posted the question correctly? It doesn't really make sense. The area between the two curves is 4 so I assumed that was the question.

Reply 13

ckfeister

Original post by notnek

I copied and pasted the entire question and yes it doesn't, cloudlearn are good at confusing me.

Reply 14

ckfeister

Original post by Muttley79

The area should be integrated with respect to y shouldn't it...

Not according to the question, its all y = (..)

Reply 15

Muttley79

Original post by ckfeister

Not according to the question, its all y = (..)

Irrelevant - what you are doing at the moment is finding the area between the curve and the x-axis.

(edited 7 years ago)

Reply 16

ckfeister

Original post by Muttley79

Irrelevant - what you are doing is finding the area between the curve and the x-axis.

Do I flip the x formulas to y or..?

Reply 17

Notnek

Original post by Muttley79

Irrelevant - what you are doing at the moment is finding the area between the curve and the x-axis.

The OP's method will work.

The questions asks for the area bounded by the two curves and the y-axis.
The OP is finding the area below the blue curve and subtracting the area below the black curve.

Reply 18

Notnek

Original post by ckfeister

...

Ignore what I said before about the question being wrong - I had pictured it incorrectly. See my post above for a proper picture.

The question is fine.

Reply 19

Muttley79

Original post by notnek

The OP's method will work.

The questions asks for the area bounded by the two curves and the y-axis.
The OP is finding the area below the blue curve and subtracting the area below the black curve.