1. ## antiderivative

Consider the function . Let be the antiderivative of with .
Then equals ?

I am having trouble with this one, this is the answer I came up with.
x(3sec^2(t)-10t^3)

Thankx
Keith

2. Originally Posted by keith
Consider the function . Let be the antiderivative of with .
Then equals ?

I am having trouble with this one, this is the answer I came up with.
x(3sec^2(t)-10t^3)

Thankx
Keith
okay, we're not integrating with respect to x, or they would have asked for F(x). there are no special rules for this one. the derivative of tan(x) is sec^2(x), so just go backwards when integrating:

f(t) = 3sec^2(t) - 10t^3
=> F(t) = int{3sec^2(t) - 10t^3}dt
...........= 3tan(t) - (5/2)t^4 + C

Now F(0) = 0
=> 0 = 3tan(0) - (5/2)(0)^4 + C
=> C = 0

so F(t) = 3tan(t) - (5/2)t^4

so i guess you were integrating with respect to x and treating the function of t as a constant....not correct i'm afraid. if they wanted you to integrate with respect to x, they would let you know explicitly

3. Originally Posted by keith
Consider the function . Let be the antiderivative of with .
Then equals ?

I am having trouble with this one, this is the answer I came up with.
x(3sec^2(t)-10t^3)

Thankx
Keith
Where did the x come from?

F(t) = Int[3*sec^2(t) - 10t^3,t] = 3*tan(t) - (10/4)*t^4 + C

For F(0) = 0 we have:
0 = 3*tan(0) - (5/2)*0^4 + C = C

Thus C = 0

Thus
F(t) = 3*tan(t) - (5/2)*t^4

-Dan