Question

Definite Integral Question!!!!

Answer 1

\[\Large \int\limits_{0}^{\pi/4}xtanx~dx\]

Answer 2

I don't think it is possible to take integral and have it expressed in elementary algebra...

Answer 3

I'm sure if my teacher wants me to show work cause i try to look up the indefintie integral of this and it's this big ol formula

Answer 4

I'm not sure

Answer 5

If I were you I'd make a list of the various methods of integration for reference and look at it often. The first impression I got here was that this particular definite integral would be a perfect candidate for integration by parts. But don't take my word for it; try integration by parts and see if you can make this method work for you.

Answer 6

I'm in Calc AB so we haven't learned Integration by parts which is why I want to know how to do it without that method.

Answer 7

Which other methods have you considered, have you tried, have you eliminated? Have you considered numerical integration?

Answer 8

I think my teacher wanted me to just my calculator cause I don't have any rules from this list that I'm supposed to use to calculate

Answer 9

It's fine, haha

Answer 10

so you can use calculator? what kind?

like I said, integral of x tanx cannot be expressed in elementary algebra.
this problem shouldn't be given to you.

Answer 11

Have you studied Riemann Sums? Have you considered using either the Trapezoidal Rule or Simpson's Rule?

Answer 12

Have you learned how to express functions such as tan x as series?

Answer 13

Have you learned how to use integration rule #10?

Answer 14

It's \(\int xtan(x) dx \), not \(\int tan(x) dx\)
there is really no product rule for integral.

though it is possible to solve with Riemann Sums

Answer 15

yeah, Riemann Sums should be used. do you know that method? @doulikepiecauseidont

Answer 16

Yes, but can you catch me up on it again?

Answer 17

We pick a number of intervals, lets just say n=4 and we split up the interval [0,pi/4] innto those intervals of \[\Large \Delta x =\frac{ \frac{ \pi }{ 4 } -0}{ 4 }\]

Answer 18

\[\Large \Delta x=\frac{ \pi }{ 16} \]

Answer 19

And then your x values would be \[x _{i}=a+i*\Delta x=0+i*\Delta x =i*\Delta x\]

Answer 20

\[\Large \frac{ \pi }{ 16 }(f(\frac{ \pi }{ 4 })+f(\frac{ 3\pi }{ 16 })+f(\frac{ \pi }{ 8 })+f(\frac{ \pi }{ 16 }))\]

Answer 21

Is that the correct set up (using a right hand Riemann sum of n=4 intervals)?

Answer 22

and your function, f(x) = x*tan x would then become\[(i*\Delta x)\tan(i*\Delta x)\] which would be easy to do with a calculator or computer but NOT with the methods you already have.

Answer 23

But is that set up correct?

Answer 24

My \[x _{i}=a+i*\Delta x=0+i*\Delta x =i*\Delta x\] DOES assume that we are using the right end point.

You would be summing up terms that resemble the following:\[(i*\Delta x)\tan(i*\Delta x)*\Delta x\]

Answer 25

OK, thanks!

Answer 26

Please note that delta x in the Riemann sums method is not a constant such as Pi/12; it's a function of n, where n is the number of subdivisions of your integral. If y ou arbitrarily choose n=4, you are using numerical approximation to evaluate your integral, and not Riemann Sums.

Answer 27

Ok,

Answer 28

You might want to refer to the following:

https://answers.yahoo.com/question/index?qid=20100125030601AA3vO51

before you invest any more time and effort into this problem.

Answer 29

Nothing wrong with using numerical methods / numerical approximations, so long as y ou undrstand that this is not the same thing as Riemann Sums, and that your result via choosing n = 4, n=10, and so on, will ONLY be approximations.

On the other hand, if you apply Riemann Sums to integrate a simple polynomial function, your result will the the EXACT area under your curve from x=a to x=b.

Good luck! I need to get off the Internet now.