Area by integration question (1 Viewer)

[alldaybaby]

okay, so I know how to integrate and everything. But I am really confused about the area I am actually trying to find in this question.

Find the area enclosed btween the curve y=x^2, the x-axis and the line y= -2x + 8.

If someone could tell me the area they are looking for in this question that would be great. The answer is 6 2/3 units^2 Thanks heaps

 

[Bored Of Fail 3]

way to easy

 

[alldaybaby]

help would be appreciated haha

 

[Bored Of Fail 3]

intersections x^2 = -2x + 8
x^2 +2x -8 =0
(x+4)(x-2) =0

x=2, x=-4

now lets a point in the interval -4<=x<=2

say x=0

now when x=0, x^2 =0 , but -2x+8 = 8

therefore the line is above the parabola

so area = integral ( top y - bottom y ) dx between limits

= integral (-2x +8 -x^2) dx from x=2 to x=-4

 

[Bored Of Fail 3]

lol nah thats wrong, I ddint draw a picture

 

[Bored Of Fail 3]

the actual area is a triangle sort of thing, if you draw it up

you will see it consists of the intergal of the line and an integral of the parabola

 

[alldaybaby]

lol nah thats wrong, I ddint draw a picture

yea i did that method but i get 36 u^2 :/

 

[Bored Of Fail 3]

x intercept of the line is x=4, and the intersection of the line with the parabola is x=2

and then we have a seperate area under the parabola from x=0 to x=2 ( the intersection point )

so = integral ( -2x + 8 ) dx [ 4..2] + integral (x^2) dx [ 2..0]

 

[Bored Of Fail 3]

= [-x^2 +8x ] [ 4..2] + (x^3 /3) [ 2..0]
= ( -16 + 32) - ( -4 +16) + (8/3) - (0) = 6 2/3

 

[hscishard]

= [-x^2 +8x ] [ 4..2] + (x^3 /3) [ 2..0]
= ( -16 + 32) - ( -4 +16) + (8/3) - (0) = 6 2/3

Still helping I see (Y)

 

[alldaybaby]

= [-x^2 +8x ] [ 4..2] + (x^3 /3) [ 2..0]
= ( -16 + 32) - ( -4 +16) + (8/3) - (0) = 6 2/3

okay thanks heaps man, I get how to do that, but like, I don't see how you gain deduce to find that area from the question :/

 

[PilotMerp]

way to easy

= integral (-2x +8 -x^2) dx from x=2 to x=-4

lol nah thats wrong, I ...

hmm

 

[Bored Of Fail 3]

hmm

lol what , I thought it was a simple top -bottom question, I couldnt be bothered drawing it at first, also what do you expect 100% undivided free help , I am listening to music and doing other stuff as well.

 

[Bored Of Fail 3]

Still helping I see (Y)

dnt know, cnt really help myself , just find it a bit hard to deny everyone help when it was only mainly the smartass MrBrightside that pissed me off

 

[Bored Of Fail 3]

okay thanks heaps man, I get how to do that, but like, I don't see how you gain deduce to find that area from the question :/

you draw a picture lol

 

[PilotMerp]

lol what , I thought it was a simple top -bottom question, I couldnt be bothered drawing it at first, also what do you expect 100% undivided free help , I am listening to music and doing other stuff as well.

cool down bro i was jk