Question

I have the answer can somone please check me....
Estimate the area under f(x)=(1/4)x^3+1
From x=0 to x=6 using 3 rectangles and left hand sums. Enter you estimates here?

Answer 1

what answer did you get?

Answer 2

I got 24

Answer 3

@electrokid is that the right answer.

Answer 4

nope

Answer 5

show your steps

Answer 6

ok 2 is the width of the triangles and then f(2) and F(4) and F(6)
2*2=4 2*4=8 2*6=12 4+8+12=24

Answer 7

hmm...
you are asked for LEFT HAND SUMS
you did the right hand ones

Answer 8

oh then how do you do teh left hand

Answer 9

so,
\[h=2\\
A=h\times\sum_{k=0}^nf(x_k)=h\times\sum_{k=0}^n\left({x_k^3\over4}+1\right)
\]

Answer 10

where \[x_k=x_0+k\times h\]

Answer 11

ok um I am a little confused h=2 and k=0 how do I know what the rest equals

Answer 12

h = 2;

\[k=0,x_0=0;f(x_0)=1\]
\[k=1,x_1=0+2=2,f(x_1)={2^3\over4}+1=?\]
\[k=2,x_2=0+4=4,f(x_2)={4^3\over4}+1=?\]
\[A=h\times[f(x_0)+f(x_1)+f(x_2)]\]

Answer 13

42 would be the answer then

Answer 14

@electrokid is that the answer 42

Answer 15

yes

Answer 16

Then should the estimate be over or under the true estimate? is the second part of the question and I can't figure it out I think it should be under

Answer 17

do you know which it should be

Answer 18

is the function continuously increasing or decreasing?
you can check with the first derivative.

Answer 19

if the function is continuously increasing, the left hand approximation is an "under approximation" and vice versa

Answer 20

ok yes it is increasing so then it is under correct

Answer 21

yes

Answer 22

ok thanks

Answer 23

yw

Answer 24

@farmergirl411 you are supposed to give a medal when you are helped