Question

Applications of the integral. Help please!

Answer 1

Here is the question.

Answer 2

@FaiqRaees can you help please?

Answer 3

so we are looking for average temperature
I believe this is an average value question
\[\frac{1}{b-a} \int\limits_a^b T(t) dt\]

where a=0 and b=8

Answer 4

so we are asked to use left endpoint rule to estimate the integral there

Answer 5

okay so well be kind of using sumnation

Answer 6

we need draw 4 rectangles between t=0 and t=8
all will equal base length

Answer 7

yes we will be summing a finite amount of things

Answer 8

Okay

Answer 9

if I want to draw 4 rectangles all with equal base between t=0 and t=8
what would the base length be?

Answer 10

n = 2

Answer 11

Is that n?

Answer 12

Delta x is the base length of rectangle

Answer 13

Or that is what is commonly used

Answer 14

oh yah sorry

Answer 15

But yes Delta x=(8-0)/4 which is 2

Answer 16

so we want to draw these rectangles starting from the left endpoint
the left endpoint is 0

so we will draw a rectangle from t=0 to t=2
then another from t=2 to t=4
then another from t=4 to t=6
then another from t=6 to t=8

Answer 17

we are going to take the left endpoint to find the heights of these rectangles because that is what left endpoint rule tells us

Answer 18

now the left endpoints alone are not the heights
but T(left endpoints) are the heights

Answer 19

So it will be circumscribed rectangles?