Question

Calculus help please?

Answer 1

No need to use calculus, right?

Answer 2

Elementary geometry can solve it. hehehe..

Answer 3

its easy find area under the cure in region x=(0,8) and that is your ans of this question

Answer 4

Recall that definite integrals can be interpreted as "areas under curves on an interval [a,b]."

for example, There's a trangle of height 3 and base 2; what is its area? What are the next two areas? Name them and determine their areas.

Then add up all four areas.

Answer 5

Note that I'm assuming that you were to find the "AREA between the curve on [0,8], where we give that negative area formed by the semicircle a - sign to make it positive.

There's a different interpretation, however: If you are to INTEGRATE this function from x=0 to x=8, then the result will be near zero, as the integral from 4 to 8 of that semicircle will be negative, countering the positive area under the graph from 0 to 4.

Decide which interpretation you believe applies here.

Answer 6

and are under the cure = (1/2)*2*3+1*3+(1/2)*1*3+(pi/2)*2^2=15/2+2pi

Answer 7

so ans is d

Answer 8

HI!!

Answer 9

the answer is certainly NOT D

Answer 10

I was thinking 15/2-2pi

Answer 11

the semi circle is below the x axis, it comes up as negative

Answer 12

@kky10997 Don't give out answers. Also it's better to not give out complete working, unless it's more explained.

Answer 13

@LorenBeech why were you thinking that? Is it a guess...?

Answer 14

sory area=-(pi/2)*2^2+15/2

Answer 15

yes -2pi+15/2 area of half circle is -

Answer 16

The problem statement calls for an INTEGRAL, not the total area between the graph and the x-axis.

Therefore, use areas to evaluate the integral: but remember that if the area is above the x-axis, that integral is positive; if below the x-axis, that part of the integral is negative.

Combine all the + and - parts to find the overall value fo teh integral.

Answer 17

No sir, not a guess. @agent0smith

Answer 18

Then show your work as to how you got it

Answer 19

I took into account what Mathmale had said previously

Answer 20

The more you share of your work, the more detailed and pertinent the feedback we can give you. You have a total of four different parts to this one graph. Show how you obtained the area of each one and how you decided whether to give a + or - sign to each.

Example: First area is a triangle of base 2 and height 3; its area is \[A _{1}=\frac{ 1 }{ 2 }(2)(3)\]

Answer 21

If you show your work, it's much easier for us to correct you if it's incorrect.

What's the area between 0-4? the trapezoid shape.

What's the area of the semicircle?

Answer 22

and we give that a + sign because the area is above the x-axis.

Answer 23

Thank you @mathmale, I understand now.

Answer 24

What's the area between 0-4? Just use the formula for area of a trapezoid, A=0.5*h*(b1 + b2)

What's the area of the semicircle?

Answer 25

My pleasure, Loren.

Note that agent0smith's suggestions are valid.

Answer 26

I saw, I can only focus on one person at a time though. It's overwhelming.