Bazza's 3/4 Question Thread

[WhoTookMyUsername]

How do i integrate 1/(1+sinx)

Its driving me insane


Ugh finally got it it D:

How can i  see what to integrate quickly ? Like what i should try and convert to?

[pi]

How do i integrate 1/(1+sinx)

Its driving me insane

dw about it, you'll never get anything that complicated in any SAC/exam without prompting on what to do next.

[Somye]

How did you do it? I'm pretty sure the solutions were wrong...

[WhoTookMyUsername]

Yeah solutions were wrong, mr g thought that it was cosx

Uh "rationalise it" then split into 2 integrals then integrate

[WhoTookMyUsername]

what is the area bound by y=ln2x , axes and y=2?

i did e^y = 2x


and then integrated with respect to y 1/2S(2,0 terminals)e^y dy is what i put
is that correct?
(my teachers answers have something random)

[b^3]

what is the area bound by y=ln2x , axes and y=2?

i did e^y = 2x


and then integrated with respect to y 1/2S(2,0 terminals)e^y dy is what i put
is that correct?
(my teachers answers have something random)

Thats they way I'd look at it, unless I've missed something. Ended up with square units.

What did your teacher do?

[WhoTookMyUsername]

full question is
The area bounded by the curve y = ln2x , the coordinate axes, and the line y =2 is given by the integral :

he put C

S((e^2)/2, 1 terminals) ln2x dx

he put worked solutions up which make some reference to the "inverse" having the same amount under the x axes but i'm not sure why he did that or whether i'm missing somethign

[Phy124]

I did;



Where the comes from



(same answer as b^3)

So yeah you guys are right (AFAIK)

edit: changed x to 2x

[b^3]

They're both valid, except at spesh level, the first way can be done by hand, the second one cannot, needs a CAS calc (or by integration by recongition in methods (which is backwards integration by parts, but you don't need to know that now...... forget I said the thing in the second level brackets)).

So if its exam 1, then you would need to do the first one.

[WhoTookMyUsername]

it was exam 2, both were options on the SAC

i think the infallible Dr. G. has made 2 mistakes in 3 of the past SACs combined

one was having 2 correct options, another was asking to prove something incorrect :O

does anyone have a good 2 (double sided) page calculus cheat sheet by any chance

[WhoTookMyUsername]

it was exam 2, both were options on the SAC

i think the infallible Dr. G. has made 2 mistakes in 3 of the past SACs combined

one was having 2 correct options, another was asking to prove something incorrect :O

does anyone have a good 2 (double sided) page calculus cheat sheet by any chance

Also

When it says evaluate the integral, do you need to account for when the equation crosses the x axis?
(im pretty sure not, but i almost made this mistake today, want to be sure)

[kensan]

When it says evaluate the integral, you just do it without worrying about the graph interesting the x-axis. But if it asks specifically for the area, then you do account for it

[brightsky]

When it says evaluate the integral, you just do it without worrying about the graph interesting the x-axis. But if it asks specifically for the area, then you do account for it

yeah, don't equate integration and area calculation. integration is but a technique that facilitates the calculation of areas under curves. so when asked to evaluate a definite integral, don't even bother looking at graphs or adding units^2. just solve it as per usual.

[sahil26]

Why does the integral of a function give the area under the graph? Is there some sort of proof or explanation?
Help would be appreciated

[brightsky]

http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus