integration using ln

melissah · December 5th 2006, 02:56 PM

Studying for my math final, and I'm having some problems with some integration questions... the first:
Integrate (bottom limit of 2, upper limit of 4) (3/x)dx
this doesn't look hard, and apparently the answer is 3ln2 but I have no idea how to get there.

The second is:
Integrate (bottom limit 1, upper limit 2) [dt/(8-3t)]
And the answer is (1/3)ln(5/2)

anyone wanna give me a hand with this?

**topsquark** · December 5th 2006, 03:17 PM

Originally Posted by melissah

Studying for my math final, and I'm having some problems with some integration questions... the first:
Integrate (bottom limit of 2, upper limit of 4) (3/x)dx
this doesn't look hard, and apparently the answer is 3ln2 but I have no idea how to get there.

The second is:
Integrate (bottom limit 1, upper limit 2) [dt/(8-3t)]
And the answer is (1/3)ln(5/2)

anyone wanna give me a hand with this?

$\int_2^4 dx \frac{3}{x} = 3 \int_2^4 \frac{dx}{x}$

= $3 (ln(4) - ln(2)) = 3 ln \left ( 2^2 \right ) - 3 ln(2)$

= $3 \cdot 2 ln(2) - 3 ln(2) = 3 ln(2)$

================================================== ==

$\int_1^2 \frac{dt}{8 - 3t}$

Let $x = 8 - 3t$ . Then $dx = -3 dt$ so
$\int_1^2 \frac{dt}{8 - 3t} = \int_5^2 dx \frac{-1}{3} \frac{1}{x}$

= $-\frac{1}{3}(ln(2) - ln(5)) = \frac{1}{3}(ln(5) - ln(2))$

= $\frac{ln(5/2)}{3}$

-Dan

Thread: integration using ln

LinkBack

Thread Tools

Display

integration using ln

Similar Math Help Forum Discussions

Integration help please these are three small even basic integration problems

sketch the region of integration and change the order of integration.

Definite Integration - Double integration by parts

Simple Integration problem: Trigonometric Integration

Tricky integration, possibly Integration Factor

Search Tags