Intergration (II) (1 Viewer)

[Lukybear]

I have two questions.

1. Find the equation of the curve COD assuming it is of the form y=ax^2n.
C(-60,18) O(0,0), D(40,8).

2.Line AB: 20y=x+480
Curve CD: y=x^2/200
A(-60,21) B(40,26)

Find the area between the line AB and the Curve CD, between x= 40, x=-60

I got 1883 1/3 but the answer has 466 2/3. Am i wrong?

 

[Timothy.Siu]

I have two questions.

1. Find the equation of the curve COD assuming it is of the form y=ax^2n.
C(-60,18) O(0,0), D(40,8).

2.Line AB: 20y=x+480
Curve CD: y=x^2/200
A(-60,21) B(40,26)

Find the area between the line AB and the Curve CD, between x= 40, x=-60

I got 1883 1/3 but the answer has 466 2/3. Am i wrong?

1. just sub in the points and solve simultaneous equations.

 

[Lukybear]

What about 2? Anyone? Its from Fitz.

 

[untouchablecuz]

I have two questions.

1. Find the equation of the curve COD assuming it is of the form y=ax^2n.
C(-60,18) O(0,0), D(40,8).

2.Line AB: 20y=x+480
Curve CD: y=x^2/200
A(-60,21) B(40,26)

Find the area between the line AB and the Curve CD, between x= 40, x=-60

I got 1883 1/3 but the answer has 466 2/3. Am i wrong?

A = S [40 --> -60] (x/20+24)dx - S [40 --> -60] (x^2/200) dx
= a-b

a = (0.5)(26+21)(40-(-60)) (area of trapezium)

b = 1400/3 = 466 2/3 (after evaluating)

.'. A = 1883 1/3 u^2 is the area enclosed

the answer gives the area under the parabola for some reason

 

[Lukybear]

Awesome. Thanks os much to the above.

 

[Lukybear]

Also if some1 can help me in this question that would be great.

Find the equation of the tangent to the parabola y=2x^2 at (1,2). Calculate its point of intersection with the x-axis and the volume of the solid formed when the area between the parabola, the tangent line and the xaxis is reveloved about the xaxis.

Especially the bit about forming a solid of revolution.

The tangent, has equn of
y=4x-2
THe pt of intersection is (1/2,0)

But the area formed i found to be 2/15 pi, which is different to the answer. Much help would be appreciated.

 

[TrueHappiness]

Yea thats what i Got too.

 

[Lukybear]

Any1 else for the above?

 

[Timothy.Siu]

Also if some1 can help me in this question that would be great.

Find the equation of the tangent to the parabola y=2x^2 at (1,2). Calculate its point of intersection with the x-axis and the volume of the solid formed when the area between the parabola, the tangent line and the xaxis is reveloved about the xaxis.

Especially the bit about forming a solid of revolution.

The tangent, has equn of
y=4x-2
THe pt of intersection is (1/2,0)

But the area formed i found to be 2/15 pi, which is different to the answer. Much help would be appreciated.

well, y'=4x=4 at (1,2)
y-2=4(x-1)
y=4x-2
y=0, x=1/2

uhh when x=0 y=-2
V=2/3pi ?

 

[Lukybear]

Timothy, but dosent it say the intesection with the x-axis? Meaning anything belwo the x-axis is discounted. If you can pleaes post solution.

 

[Timothy.Siu]

Timothy, but dosent it say the intesection with the x-axis? Meaning anything belwo the x-axis is discounted. If you can pleaes post solution.

hmm? what do u mean by anything below the x-axis is discounted?
i just did the solid of revolution.

i actually didn't integrate it, i just did the volume of a cone.

 

[Lukybear]

What... you didnt integrate it. How did you solve it then?

What i meant was that the tangent cut the y-axis below at y = -2. Thus the area between the parabola and the tangent and x-axis, is above the x-axis.

Otherwords my workings...




But also, how would volume of the cone work? The parabola is curved.

 

[Timothy.Siu]

oh, it was area between parabola.
my answers totally wrong then.
this is tricky then.

 

[Lukybear]

zzz... but how did u get 2/3pi. Because that was the right anwer.

Im just curious and want to know.

 

[Timothy.Siu]

it should be,

pi S [4x^4-(4x-2)^2] dx from 0.5 to 1

+ pi S (4x^4)dx from 0 to 0.5

 

[Lukybear]

Wait a second. Isnt mine intergration also right?

 

[Timothy.Siu]

Wait a second. Isnt mine intergration also right?

yep, that should be right, except ur limits are switched around on the 2nd one? maybe

 

[Lukybear]

Na, I done it ur way. Got the same answer.

Thanks for the help.