Question

I've got downs please help me integrate this function (: metals!

Answer 1

is h'(x) asked ?

Answer 2

Are you SURE you need that integral or do you actually need \(\dfrac{dh}{dt}\)?

Answer 3

yes i forgot to add that, h'(x)..i forget easily

Answer 4

have you learnt the fundamental theorem of calculus ?

Answer 5

Please double-check the instructions. The function you've given here is a definition by incomplete integral. I suspect that your problem statement asks you to find the derivative of h(x).

You might want to check the name of this Theorem: I think it's Fundamental Theorem of Integral Calculus, Part I, involving a function defined as an integral. See...hartnn has brought up the same possibility.

What does this Theorem tell us?

Answer 6

Catalog:
---- I've got downs
---- i forget easily

I have a plan. Just STOP saying, thinking, believing, or suggesting any such thing. Why not learn some mathematics and never again make an excuse why you cannot succeed?

Answer 7

\[\int\limits_{b}^{a}f(x)dx=F(b)-F(a)\]

Answer 8

Please refer to your text quickly and determine how you find the derivative of a function which itself is defined as a definite integral. Have you worked with this type of problem before?

Please look at the following:

http://math.ucsd.edu/~wgarner/math20b/ftc.htm

Fundamental Theorem of (Integral) Calculus, Part I.

Answer 9

I appreciate your looking up "Fundamental Theorem." What you've typed out is Actually Part II of that Theorem; Part I applies to the math problem you've posted.

Answer 10

i have done this problem i just have a tough time trying to integrate b

Answer 11

ok that makes more sense

Answer 12

Actually, there's no integration involved here, EXCEPT that your function h(x) is DEFINED as an integral. But your goal is not to integrate; rather, it's to differentiate h(x).

Answer 13

got it, ive been skipping around doing homework from different sections(up to area between curves) and i guess i looked at the problem the wrong way and saw the integral and though integration

Answer 14

thought*

Answer 15

In its most basic form the Fund. Thm. of Calculus, Part I, says that the derivative of h(x), where \[h(x) = \int\limits_{a}^{x}f(t) dt, is ~simply~ f(x).\]

Answer 16

So, \(\dfrac{d}{dt}\int\limits_{a}^{r(x)}f(t)\;dt = \dfrac{d}{dt}F(r(x)) - \dfrac{d}{dt}F(a) = f(r(x))\cdot r'(x)\)

Answer 17

the problem you have posted is slightly more complicated, because you are integrating not from a to x but rather from -5 to the function sin x. Note how tkhunny has inserted r '(x) in his final expression? That r '(x) ios the DERIVATIVE of function r(x).

Answer 18

so cos(x)

Answer 19

I ask you to assess where you are now. Look at the Fund. Thm. of Calc., Part I. Look at tkhunny's suggestion. Then try to put together the answer to your own posted math question. (Yes, the derivative of sin x is indeed cos x.)

Answer 20

ok gimme a sec and let me solve, ill be back in a minute. thanks for the advice

Answer 21

Once more:

The Fund. Thm. of Calc., Part I, applies in two diff. situations: (1) when h(x) is defined as the integral of f(t) from a constant (such as a) to the simple, stand-alone variable x; and (2) the case you have: h(x) is def. as the int. of f(t) from a to some function of x. In the latter case you must use the Chain Rule, which tkhunny has demonstrated in his formula, above.

Answer 22

ok so ((cos(sin(x))^7)*cos(x)

Answer 23

that's not correct

Answer 24

Almost. You have one more pair of parentheses than you need, and that ^7 applies ONLY to the sin x function, not to the cos function. Can you fix this?

Answer 25

And one other thing, which I, too, have overlooked: see that " t " following (x^7)? What are you supposed to do with that t?

Answer 26

can i get a hint?

Answer 27

You have:\[..... ( \cos (t^7) + t). Wherever you see " t ", you must substitute \sin x.\] Wherever you see " t ", you must substitute sin x.

Answer 28

cossin(x^7)*cos(x)+sin(x) ?

Answer 29

\[Is ~h'(x) =cossin(x^7)*\cos(x)+\sin(x) ?\]

Answer 30

You're on your way, but this expression needs some fixing up:

\[cossin(x^7)*\cos(x)+\sin(x)\rightarrow \cos [(\sin x)^7+\sin x]\cos x\]

Answer 31

Compare our answers. Notice how we MULTIPLY by cos x at the end (not add). Let me know if you're still unsure about this result. Note, however, that I need to get off the Internet now; I will be back later. There are plenty of other capable people on OpenStudy who could likely answer similar questions.

Answer 32

thanks so much!

Answer 33

i wish i could give you another medal xD

Answer 34

My pleasure. Seriously: Happy studying!

Answer 35

damn. wht man u in?