Question

Let f(x)= integral of (t^2+2t+2)dt within limits 0 to x where x is set of real numbers satisfying the inequation log(1+√6x-x^2-8)>=0.
If f(x)€[a,b] then maximum value of |a-b| is

Answer 1

@freckles

Answer 2

@ikram002p

Answer 3

You could start by solving the integral.

Also consider: \[\log(X) \ge 0 \]is true when \[X \ge 1\] for real numbers.

Answer 4

That gives me x€[2,4]

Answer 5

For the condition of log to be greater than

Answer 6

0

Answer 7

Is it sqrt(6)x or sqrt(6x) in your inequality?

Answer 8

The surd is over the whole term
6x-x^2-8 whole of if

Answer 9

It*

Answer 10

x€[2,4] is correct for the inequality, yes..

Answer 11

since g(t)=t^2+2t+2 is an increasing function and all above the x-axis
then the area in increasing as we move to the right of x=0
Since x can only be between x=2 and x=4
then that would mean that
\[\int\limits_0^2 g(t) dt \le f(x) \le \int\limits_0^4 g(t) dt\]
so you will find a and b by evaluating both of those integrals I believe

Answer 12

that is increasing function on the interval [0,4] which is all we need to be concerned with

Answer 13

of course it is increasing elsewhere but that is the only interval as I said we should be worried about

Answer 14

Bt when we r gonna solve the integral won't there come a constant ...
How to evaluate its value?

Answer 15

@ganeshie8

Answer 16

@hartnn

Answer 17

I'm not sure what you are asking

Answer 18

we already know that \[f(x) \in [\int\limits_0^2 g(t) dt, \int\limits_0^4 g(t) dt]\]
so you already know your a and b
you just have to evaluate those integrals

Answer 19

g(t) was equal to your integrand
g(t)=t^2+2t+2

Answer 20

It's integration is t^3/3 + t^2 + 2t +c what about the value of c?

Answer 21

you have a definite integral

Answer 22

not an indefinite

Answer 23

Oops !! Forgot that sorry for asking a stupid question as that!!
Thanks also

Answer 24

however you could put plus C in but the C's are just going to cancel out when you do the subtraction part

Answer 25

\[a=[\frac{t^3}{3}+t^2+2t]_0^2 =? \\ b=[\frac{t^3}{3}+t^2+2t]_0^4=?\]

Answer 26

a=32/3
Ans b=136/3

Answer 27

And*

Answer 28

@freckles thankyou

Answer 29

np