Intergration

what do mean? show me, please...

Original post by RDKGames

You don't really need to explicitly integrate anything.

First part of this kinda important theorem is what you want: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Formal_statements

Reply 5

Original post by Tom123123123

what do mean? show me, please...

Do you not see the relation between FToC and your problem??

Reply 6

So F(x)=the integral
and F'(x)=f(x)
and how does that help me?

Reply 7

Original post by Tom123123123

So F(x)=the integral
and F'(x)=f(x)
and how does that help me?

Because in your case,

I(a)

is your

F(x)

and

4-2^{x^2}

is your

f(t)

...

The problem can be reformulated using the variables in the theorem;

I(x) = \displaystyle \int_0^x 4-2^{t^2} .dt

and you seek

I'(x)

. [Just, yknow,

b

in the place of

x

]

(edited 5 years ago)

Reply 8

could you just show me, I'm really lost

(so f(t)=F(a)-F(b))

Reply 9

Original post by Tom123123123

could you just show me, I'm really lost

(so f(t)=F(a)-F(b))

Not really sure what is difficult about it?

Using the theorem the answer is

I'(b) = 4-2^{b^2}

to the differentiation bit of the question.

so the answer is ±1

Original post by Tom123123123

so the answer is ±1

Not quite that either.

Reply 12

but I want I'(b) to =0 ?

Reply 13

then b would equal ± square root 2

Reply 14

Original post by Tom123123123

but I want I'(b) to =0 ?

I know... I'm saying those values of

b

don't make this hold.

b=\pm \sqrt{2}

as you say above.

Though things to note;

- I forgot the question used

a

so I used

b

in its place... it's still the same ideas.

- Since the lower limit of the integral is zero, I'd think you disregard the -ve solution. Context is needed tbh.

- Have you even covered FToC? You seem majorly lost on a problem that is trivial given the theorem.

(edited 5 years ago)

Reply 15

Notnek

Original post by Tom123123123

For a positive number a let:
https://imageshack.com/a/img922/2403/LY27l9.png
for what values of a is dI/da=0

help please

Can I ask what level of maths you're doing e.g. A Level / degree?

Reply 16

further maths- the teacher has not taught us anything :wink:

Reply 17

Notnek

Original post by Tom123123123

further maths- the teacher has not taught us anything :wink:

Which exam board? And where did you get this question from?

Reply 18