Question

help calc

Answer 1

@Vocaloid

Answer 2

I know 1 part a is -0.45 because we are told the answer but not sure how to get it

Answer 3

you just need to make 4 intervals between 0 - 2 and pick the midpoint of each interval. find the value of the function at that interval, then add them up.

Answer 4

so 1,1.25,1.5,2? work

Answer 5

the integral starts at 0.

Answer 6

okay 0,.5,1,1.5,2

Answer 7

crap that's 5

Answer 8

0,1,1.5,2 work?

Answer 9

what you had before was fine

0-0.5
0.5-1
1-1.5
1.5-2

Answer 10

midpoints
.25
.5
.75
1?

Answer 11

the middle of 0 and 0.5 is 0.25
the middle of 0.5 and 1 is 0.75
the middle of 1 and 1.5 is 1.25
the middle of 1.5 and 2 is 1.75

Answer 12

oh right duh I was doing the large numbers

Answer 13

so what do I do next?

Answer 14

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
you just need to make 4 intervals between 0 - 2 and pick the midpoint of each interval. find the value of the function at that interval, then add them up.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 15

evaluate the function at the midpoints. this will give you the height of each rectangle. then multiply height *width of the interval to give the area of each rectangle.

Answer 16

\[\int\limits_{0}^{2} \ln .25 xdx like this?\]

Answer 17

you should not be taking an integral here

Answer 18

width of each interval is 0.5

ln(0.25)(0.5) + ln(0.75)(0.5) + ln(1.25)(0.5) + ln(1.75)(0.5)

Answer 19

yay I got -.45

Answer 20

so part b how would I answer it?

Answer 21

the function is decreasing so the left estimate over-estimates the function (see the middle graph)

Answer 22

*the left graph sorry

Answer 23

ty only 5 questions left after this question 3 are graphing things

Answer 24

@Vocaloid what do I do for 2?

Answer 25

notice how the limit definition is a sum of rectangles, defined by e^sin(x) which gives the height, and deltax that gives the width of each rectangle

so the function itself is just e^sin(x), set up the integral with (a) as the lower bound and (b) as the upper bound

Answer 26

these are the other questions once we finish 2

Answer 27

I mean for 3-6 they're self-explanatory, just graph the function and divide the area into shapes, take the sum

Answer 28

\[\int\limits_{-1}^{12} e^\sin(x) is this \it?\]

Answer 29

2 is just setting the equation up right?

Answer 30

yeah

Answer 31

so 3 I have 2pi+4 how should I divide the graph?

Answer 32

did you sketch the graph? just start dividing the area into boxes or triangles or whatever

Answer 33

yes and okay that works for me

Answer 34

so 5 I graph and solve equation algebraically?

Answer 35

uh I think you just divide the area under the graph again

Answer 36

idk maybe they just want you to take the integral

Answer 37

idk but 5 and 6 am kinda lost lol

Answer 38

the answer to 5 is 14 just gotta figure out how to get it

Answer 39

\[\int\limits_{1}^{4}3\sqrt{x}dx\] should do it

Answer 40

if that isn't the what they want, then just divide the area under the curve into triangles/rectangles, etc.

Answer 41

yay answer is 14 ty

Answer 42

how would I do 6?

Answer 43

uh well just sketch the graph, sketch the x-axis, and shade the area between them
then divide that area into rectangles/etc. and find the sum of that area

Answer 44

I graphed the equation could you show me the shading so I don't mess it up

Answer 45

6 is 8/3 but how do I get that answer?

Answer 46

sketch the equation. shade everything that's below the equation and above the x-axis.

Answer 47

divide the region into rectangles and take the sum.

Answer 48

were does the 0,3 come in?

Answer 49

sketch the graph across the domain (0,3)

Answer 50

I am graphing y=x^2-2x right just checking?

Answer 51

yes.

Answer 52

okay so now I'm dividing the region
but I want to make sure I get the answer 8/3

Answer 53

have to show my steps algebraically

Answer 54

@Vocaloid

Answer 55

I'm trying to think

Answer 56

that's what my graph looks like basically

Answer 57

if you want the exact answer 8/3 you need to take the integral of the function from 2 to 3 since that's where the shaded region is

Answer 58

I got 4/3 with 3 on top 2 at bottom and equation dx?

Answer 59

you need to re-calculate the integral

Answer 60

where did I mess up?

Answer 61

you must have made an algebraic mistake when you were calculating the integral.

Answer 62

ugh hold on

Answer 63

just realized they want the total area so you'd also have to find both of these regions

Answer 64

so you would have to find the absolute value of the integral between 0 to 2, then the integral from 2 - 3

Answer 65

I'm not 100% sure what they mean by finding the area algebraically, they probably want a Riemann sum where you divide the area into rectangles like you did in problem 1. this won't get you the exact answer, but an estimate.

if you want the exact answer you need to take the integrals.

Answer 66

that works ty and for the last question

Answer 67

well, for the riemann sum you construct a series of rectangles that estimate the area under the curve, right?

when you take the limit as the size of the intervals approach 0, you get an infinite number of rectangles, and summing these rectangles will give you the definite integral