Question

If f is a continuous function such that
∫^x f(t)dt=(3x)/4x^(2)+5)
0
find the value of f(1)

Answer 1

Differentiate both sides w.r.t x
so that you can use,
\(\huge \frac{d}{dx} \int \limits_0^x f(t)dt=f(x)\)
hence you get f(x) by differentiating.
then just put x=1 in it.

Answer 2

u understand what u need to do ? @paitucker

Answer 3

so after you differentiate and get 3/8x what do i do?

Answer 4

oh, there you need quotient (u/v) rule,
you cannot just diff. numerator and denominator separately.

Answer 5

\(\huge \frac{3x}{4x^2+5}\)
is the question, right ?

Answer 6

yes

Answer 7

know how to use quotient rule ?

Answer 8

yeah,im trying right now

Answer 9

(4x^2+5)(3)-24x^2/16x^2+25 ?

Answer 10

the denominator is incorrect

Answer 11

it should be (4x^2+5)^2
don't simplify it.

Answer 12

numerator is correct :)

Answer 13

thanks :) , what should I do after that?

Answer 14

so u have f(x) = .....
to find f(1), just put x=1 in that.

Answer 15

f(x)=[(4x^2+5)(3)-24x^2]/(4x^2+5)^2
put x=1

Answer 16

5/81 ?

Answer 17

numerator = (4x^2+5)(3)-24x^2 = (4+5)*3-24 = 9*3 -24 = 27-24 = 3
denominator = 81 is correct.

Answer 18

got your error ?

Answer 19

so its 3/81 = 1/27

Answer 20

ohh okay :) I get, thanks!!

Answer 21

welcome ^_^