Question

So using the fundamental theorem of calculus part1 if I have an integral function were the top is (ln x) the bottom 3 and then beside it it is sint dt! I have the answer as
=sin ln x * 1/x
Is this correct??

Answer 1

Can anyone help??

Answer 2

Shonie:

This is slightly off the point, but anyway: Are you able to integrate the function f(x) = sin x? Please look this integral up in your textbook or other reference if you're not sure.

Supposing you integrate f(x) = sin x and obtain F(x) = ????

Then the "definite integral" of f(x) from 0 to Pi can be evaluated as the following:

F(Pi) - F(0). Try it.

Now, back to YOUR initial question: I find your presentation of this integral difficult to follow as you've phrased it: "an integral function were the top is (ln x) the bottom 3 and then beside it it is sint dt". First: Did you intend to convey an indefinite integral or a definite integral? (An indefinite integral would have no limits of integration, whereas a definite integral would.) If you're required to apply the Fundamental Theorem of Calculus, I suspect you're dealing with a definite integral.

If so, what are your limits of integration? I suspect you're attempting to integrate the function sin t with respect to t from lower limit 3 to upper limit ln x. Is that correct?

If so, try phrasing your question like this: "evaluate the definite integral of sin t with respect to t over the interval 3 to ln x".

Using carefully chosen mathematical language in describing problems may actually lead to your understanding those problems better, as well as bring in more responses when you post a question to OpenStudy.com.

Answer 3

Unfortunately, your "sin ln x * 1/x" is not a possible outcome of application of the Fundamental Theorem of Calculus. This Theorem would produce a result that involves subtraction: e. g., F(b) - F(a).

Please go back to my original suggestion: Find the definite integral of sin t with respect to t from lower limit 0 to upper limit Pi/2. If done correctly, your result will involve subtraction (that is, subtraction of F(0) from F(pi).

Answer 4

So... Sin ln x- sin 3??

Answer 5

Is that closer to the answer?

Answer 6

Shonie: Please focus on my previous suggestion: "Supposing you integrate f(t) = sin t and obtain F(t) = ???? "

Once you have F(t), apply the Fundamental Theorem of Calculus by evaluating F(ln x) - F(3).