Question

Q. Find the area under the curve of:

Answer 1

y (x) = x(1-x) between x = 0.5 and x = 1

Answer 2

\[\int\limits_{0.5}^{1}x(1-x)\] It will be an integral to solve ...

Answer 3

Taking (1-x) as U?

Answer 4

...just multiply x by 1-x and work the poly

Answer 5

Could you elaborate mate? :)

Answer 6

what is x(1-x) ? this is just simple algebra

Answer 7

x - x^2

Answer 8

good, then its just some basic power integrations

Answer 9

This Q is on my engineering technological maths exam, so I expected it to be harder than it looks :D

Answer 10

but why? its just an engineering book lol

Answer 11

Do you mean integrate the x-x^2 yeah?

Answer 12

x = x^2 / 2 eg

Answer 13

yep, add1 and divide is the basic power rule

Answer 14

Then fill it the bounds?

Answer 15

and recall:\[\int_{a}^{b}f(x)~dx=F(b)-F(a)\]

Answer 16

Yes

Answer 17

so, what do you get, so we can chk if its right :)

Answer 18

\[[\frac{ x^2 }{ x } - \frac{ x^3 }{ x } ]\] for (b) minus the same equation for (a)

Answer 19

\[f=x-x^2\]
\[F=\frac12x^2-\frac13x^3\]

F(b): F(a):
\[(\frac121^2-\frac131^3)-(\frac12.5^2-\frac13.5^3)\]
\[(\frac16)-(\frac18-\frac1{24})\]
etc

Answer 20

Could I leave the equation as x^2 /x - x^3/3 and fill in for the bounds

Answer 21

x^2 / 2 not x^2/x

and what do you mean by "fill in for the bounds"?

determine F(b) , then determine F(a) using the function F(x) that was integrated

then subtract F(a) from F(b)

Answer 22

I'm on the same page.

Thank you Amistre! May I ask you one other thing quickly? Will help me hugely for my exam.

Answer 23

sure, as long as i got time to study for my sociology final ...

Answer 24

LOL! Really quick

Answer 25

Q. Find the mean value of the function f (t) = \[10e^{-2t}\] between t = 0 and t = 2.5

Answer 26

if i recall correctly, it is the value of f(t) that would create the same area but with a level line