- #1

Zman

- 96

- 0

## Homework Statement

I wish to find the area under the curve y = 1/2^x between x=0 and x=1 but get an answer that is half the expected answer.

## Homework Equations

Integrate y = 1/2^x to get -1/(2^x ln2) + Const

This integration result was confirmed on Wolfram

Slot in the range x = 0 to x = 1

Area = 1/ln2 (1 - 0.5) = ~0.34

## The Attempt at a Solution

But when I look at the curve of y = 1/2^x

I can see that the area under the curve between x=0 and x = 1 is double

i.e. ~0.68The range of the curve y = 1/2^x that I am interested in starts at point (0,1) and goes to point (1, 0.5)

A rough visual calculation of this area is made up of the lower rectangle 1 x 0.5 added to the area of the upper triangle (1x0.5)/2 = 0.25 which gives an approximate answer of 0.75I seem to be missing a factor of 2 as regards the integral and am at a loss.