Question

how can i find the area under the graph ln(x) using integral function? can somebody help me, and thanks in advance.

Answer 1

sorry, what is the function of the line?
ie f(x) = ln(x) ?
and between what x coordinates / limits do u want the area to be?
ie max x value, min x value...?

Answer 2

...? @iraaaaa

Answer 3

sorry for the vague question. for example, ln(x)=∫max value is 2, and min value is 1. but my equation involves exponential

Answer 4

ok, so write the exponential equation here and we'll work it out together

Answer 5

\[\ln(x)= \int\limits_{1}^{2} (1/t) dt\]

Answer 6

ok, so integral of 1/t = ln(t) + a constant
constant is negated in the presence of limits

Answer 7

integral of 1/t = ln(t) + constant

\[\int\limits_{1}^{2} (1/t) = [\ln(t) + C]\lim_{2 \rightarrow 1}\]

\[= [\ln(2) +C] - [\ln(1) +C] = \ln2 - \ln1\]

Answer 8

= 0.6932...ish = ln(x)

Answer 9

i'm not sure if i'm helping here... @ganeshie8 u got a sec?

Answer 10

do we have to insert the constant C and the limit even if they're probably not needed?

Answer 11

no, its just good to get in the practice to always remember to write the canstant in as you're not always dealing with limits

Answer 12

could you please look over this @.Sam. Im not sure?

Answer 13

http://www.vias.org/calculus/04_integration_04_05.html

Answer 14

by integrating, you are working out the area under the graph

Answer 15

so, integrating will give out the area? i'm gettin it.
btw,
what's the difference between 'ln' and 'e' ?

Answer 16

ln is natural log = log to base e
e = 2.71828182845904...etc, its a mathematical constant

Answer 17

they're kinda like opposing opporators, think plus and minus
+ opposite of -

so if u had e^10
the natural log of e^10 = ln e^10 = 10