Simpson's rule

[aj898989]

I=the integration of 3^x between the limits 6 and 2
(a) Use Simpson's rule with four intervals to obtain an estimate for I
For this question is got 660, could someone please check this and tell me if I'm correct
(b) By writing 3^x in the form e(lnk)x, where k is a constant, find the exact value of I
This confuses me, I don't know how to write 3^x in this form. I do know how to integrate 3^x on its own but we have to use the method stated.
(c) Use your answer to parts a and b to show that ln3=12/11

 

[Deleted member 4993]

I=the integration of 3^x between the limits 6 and 2
(a) Use Simpson's rule with four intervals to obtain an estimate for I
For this question is got 660, could someone please check this and tell me if I'm correct
(b) By writing 3^x in the form e(lnk)x, where k is a constant, find the exact value of I
This confuses me, I don't know how to write 3^x in this form. I do know how to integrate 3^x on its own but we have to use the method stated.
(c) Use your answer to parts a and b to show that ln3=12/11

use wolfram alpha to check your numerical answer.

for part (b), use:

y = e^[ln(y)]