Question

Calc help!!

Answer 1

The formula for the area of a rectangle is base * height.
delta x * f(x)
Start from the left point.
(3-1)*4 + (4-3)*8 + ...
can you finish it?

Answer 2

I'm confused still

Answer 3

@ganeshie8

Answer 4

Hi

Answer 5

hi!

Answer 6

Maybe start by "writing out" the 6 intervals of x

Answer 7

Look at the given table,
how many x values are given ?

Answer 8

7

Answer 9

good, what are they

Answer 10

1, 3, 4, 6, 7, 9, 10

Answer 11

right, imagine those numbers on a real line.

1 --> 3 is the first interval
3 --> 4 is the second interval
4 --> 6 is the third interval
etc

can you write out the remaining 3 intervals ?

Answer 12

6-->7
7-->9
9-->10

Answer 13

those intervals form the "width" of the rectangles
and we still need to pick the height for each of them

Answer 14

look at first interval :
```
1-->3
```

what's the value of the function at the left end point of the interval, x=1 ?

Answer 15

4?

Answer 16

yes, and the width of the interval is 3-1 = 2

whats the area of the rectangle with width=2, height = 4 ?

Answer 17

8

Answer 18

Correct. 8 is the approximate area in the first interval

Answer 19

similarly can you find the approximate ares for the remaining 5 intervals ?

Answer 20

Yes, hold on!

Answer 21

1st int: 8
2nd int: 8
3rd int: 12
4th int: 10
5th int: 24
6th int: 16
Is this correct?

Answer 22

first four are correct
last two are wrong

try again

Answer 23

you need to use the function value at left end point for the height

Answer 24

5th int: 20
6th int: 12

Answer 25

Looks good! add them up to get an estimate for the given definite integral

Answer 26

Ok, I got 70

Answer 27

Will this be my answer?

Answer 28

Looks good!

Answer 29

Thanks so so much!!!

Answer 30

yw