# Integration Question I have a midterm in 45 mins AH!

1. Jan 24, 2007

### deerhake.11

Integration Question.. I have a midterm in 45 mins!! AH!

1. The problem statement, all variables and given/known data

integral with bounds [5,x^2] of f(t)dt = (5x^2)/(x^4+6) + C

f(t) = ?
C = ?
2. Relevant equations

Uhm.. I don't know. Im guessing you have to use the FTC.

3. The attempt at a solution

I've have tried so many different types of substitution and stuff with no luck. I really have no idea what method is required to solve this; I dont remember learning it.

2. Jan 24, 2007

### Schrodinger's Dog

Probably way beyond me but have you tried partial fractions? And substitution?

Can you show what you've tried?

Last edited: Jan 24, 2007
3. Jan 24, 2007

### quasar987

The FTC says that

$$\int_a^b f(t)dt = F(b)-F(a)$$

where F'(t)=f(t).

So you want to find which function F(t) is such that F(x²) = -(5x^2)/(x^4+6). Then differentiate it to get f(t). About C, well C=F(5), so once you get F(t), finding C is a formality.

4. Jan 24, 2007

### HallsofIvy

Yes, the derivative of [tex]\int_a^x f(t)dt[/itex] is f(x). But you are given $\int_a^{x^2} f(t)dt$. Let u= x2 and use the chain rule: $\frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$.

To determine C, let x= some convenient value and evaluate.

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