Find the most general antiderivative of f(x)=–8e^x–6secant^2(x), where -pi/2<x<pi/2
Note: Any arbitrary constants used must be an upper-case "C"
F(x)=?
Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus.
intergral s^2/(1+3s^4) ds from sqrtx to 1
F'(x)=?
2 answers
∫[√x,1] s^2/(1+3s^4) ds
Are you sure there's no typo here? As you can see here
http://www.wolframalpha.com/input/?i=%E2%88%ABs^2%2F%281%2B3s^4%29+ds
this is not an integral I'd expect to find. If you meant
∫[√x,1] s^3/(1+3s^4) ds
then it's a lot easier:
1/12 log(1+3s^4) [√x,1]
= 1/12 (log(1+3x^2)-log(4))
= 1/12 log((1+3x^2)/4)
Are you sure there's no typo here? As you can see here
http://www.wolframalpha.com/input/?i=%E2%88%ABs^2%2F%281%2B3s^4%29+ds
this is not an integral I'd expect to find. If you meant
∫[√x,1] s^3/(1+3s^4) ds
then it's a lot easier:
1/12 log(1+3s^4) [√x,1]
= 1/12 (log(1+3x^2)-log(4))
= 1/12 log((1+3x^2)/4)
1 answer