Question

calculus question

Answer 1

http://gyazo.com/6f72cc9036c7d676d368b5c733089830

Answer 2

how do i start? im stuck cos of the limit \(h(x)\)

Answer 3

I can't see the whole question!

Answer 4

thats the whole question

Answer 5

http://gyazo.com/4cc1852726bfa44f3abe0fe15d3c45d9

Answer 6

Would the derivative of an integral just be the same? sqrt(t^2+4)?

Answer 7

but im confused with the limit \(h(x)\)

Answer 8

I would think it'd be this:
\[\sqrt{(h(x))^{2}+4}*h'(x)\]
Derivative of an integral using the fundamental theorem of calculus. Let the upper limit of an integral be h(x) like so:
\[\int\limits_{0}^{h(x)}f(x)dx\]
Then the derivative of this function is:
\[f(h(x))*h'(x)\]

Answer 9

i.dont.get.it.sorry!

what about the \(4\)?

Answer 10

i think i have to let \(u= h(x)\)?

Answer 11

Nah, this isn't really integration at all. I mean it is, but when it wants the derivative of an integral, we are just measuring the change of the function as it goes from the lower limit to the upper limit ofintegration. So there is no real u-sub, raise the power etc. It's just kind of a formula for it. You COULD integrate it and then take the derivative at the very end, but you'd get the same answer for infinitely more effort. It's best to just remember theprocedure for how to solve them:

\[\frac{ d }{ dx }\int\limits_{0}^{h(x)}f(x)dx = f(h(x))*h'(x)\] Whatever your upper limit of integration is, plug that into every x in your original function, then multiply everything by the derivative of whatever that upper limit is.

Answer 12

Newton lebinz :)

Answer 13

thank you!

Answer 14

Mhm ^_^