Question

A Difficult Calculus Problem

Answer 1

Let \[\huge f(x) = \sqrt[3]{x^2+4x}\]
and let g(x) be an antiderivative of f(x). Then if

g(5) = 7
find
g(1)

Answer 2

?

Answer 3

dude find the antiderivative of f(x) and then plug in g(1)

Answer 4

because g(x) = anti derivative of f(x)

Answer 5

yeah good luck with that program

Answer 6

I can't even find a u sub for this :S

Answer 7

-______________________________-

Answer 8

basically you can never find a closed form anti derivative

Answer 9

no comment

Answer 10

not yet, although i am wondering if it is some simple gimmick that i do not see
i.e. one hook that gets it

Answer 11

T_T

Answer 12

stuck

Answer 13

hint? or would a hint give it away?

Answer 14

forget it... I'll write impossible or what are you doing to my brain? ^^

Answer 15

I believe this is a non-elementary integral

Answer 16

I'll give a hint because I was completely stuck too, it's definitely not kick-you-in-the-crotch spit-on-your-neck obvious, even after seeing the solution.

Let h(x) = g(x) - 7

You'll also need a calculator for a definite integral.

Answer 17

Is the answer g(1)=-3.88222?

Answer 18

that is one hell of a hint!

Answer 19

\[h(5)=\int_a^5\sqrt[3]{x^2+4x}dx-7=0\] doesn't do much for me
i tried with wolfram to make the integral 7 and i'll be damned if i can
gotta start a bit to the left of \(-4\) but i can't figure out how much

Answer 20

You're on the right track, kinda. Want another hint?

Answer 21

Aproximate
\[
\int_0^5 f(x) dx + k =7\\
12.1265 + k =7\\
k= 7-12.1265=-5.12645\\
\int_0^1 f(x) dx + k=1.24425- 5.12645\approx -3.88
\]

Answer 22

yeah another hint would be good, because all i am doing is numeric exercise

Answer 23

@satellite73 see my solution. It is correct.

Answer 24

This problem is a numerical exercise

Answer 25

ok i thought the answer was going to be something like \(-\pi\)

Answer 26

No, it's not that fancy, but I mentioned above you'd need a calculator for a definite integral. Since it's been solved in a similar way, here's the solution they used: http://ltcconline.net/greenl/courses/105/antiderivatives/DifficultProblemSolution.htm

Answer 27

surely this is easier to tackle head-on?$$g(x)=\int f(x)\ dx\\g(5)-g(1)=\int_1^5 f(x)\ dx\\g(1)=g(5)-\int_1^5 f(x)\ dx\\
g(1)=7-\int_1^5\sqrt[3]{x^2+4x}\ dx\\g(1)\approx7-10.8822=-3.8822$$