Had a test today. Please help

hey guys,
just cam back from uni. had a test which is like 15% of my cw. pretty confident but just some question that if you can confirm i got right that'll be great.

1)

8x\sqrt (x^2 + 1) dx

integration by substitution between x=o (lower limit) and x=1 (upper limit). Did anyone get 6?

2) can;t remember exactly by if you have something like

y= \frac{some function}{2} + 2x

, to find dy/dx will you just use the quotient rule to find the first part and then "+ 2"?

thanks

Reply 1

username167718

I could be wrong, but I think:

1) Answer = (8/3)*2^(3/2). After integrating, I got (8/3)(x^2+1)^(3/2) -- what did you have?

2) You could use the quotient rule, but it would be a bit pointless. Just differentiate the numerator, then divide it by 2.

Reply 2

Mr M

Study Forum Helper

Prokaryotic_crap

hey guys,
just cam back from uni. had a test which is like 15% of my cw. pretty confident but just some question that if you can confirm i got right that'll be great.

1)

8x\sqrt (x^2 + 1) dx

integration by substitution between x=o (lower limit) and x=1 (upper limit). Did anyone get 6?

2) can;t remember exactly by if you have something like

y= \frac{some function}{2} + 2x

, to find dy/dx will you just use the quotient rule to find the first part and then "+ 2"?

thanks

I'm afraid your first answer is wrong. There is a surd in the answer.

\frac{8(2\sqrt2-1)}{3}

There is no need to use the quotient rule on the second question (although you should have got the correct answer even if you did).

\frac{dy}{dx}=\frac{1}{2}\frac{d(some function)}{dx}+2

Reply 3

Necro Defain

Oops garbage, damn internet lol. Ignore this post please

Reply 4

Necro Defain

I got the answer as (16*sqrt(2))/3 - 8/3 for the first one

Reply 5

Prokaryotic_crap

y = 8x \sqrt(x^2 +1) dx

u= x^2+1

\frac{du}{dx} = 2x

dx= \frac{du}{2x}

x= 1

u=2

x=0

u=1

Unparseable latex formula:

8(u -1)^\frac{1}{2} u^\frac{1}{2} \frac{du}{2(u-1)^\frac{1}{2}

simplyfying that and subbung u=2 and u=1 and then taking the latter from the former will give 6 i'm sure. anyone who disagrees please post working. it'll really help.

Reply 6

Necro Defain

u = sqrt(1+x^2), udu/dx = x, dx = u/x * du substitution into the integral and you get 8u^2 du to integrate and your limits become u=1 to u = sqrt(2)

Reply 7

Prokaryotic_crap

i have just realised my mistake, and to make things worse i have just realised that i had written the right thing and then just crossed it out and written something else. I want to kill myself right now