Math Help - confusion with a question about integrals, multiple choices

Hi.

Given

and

the value of
is:

A. a+b
B. 2a-b
C. a-b (which I think is right)
D. a-2b
E. b-a (might be true?)

I am confused because the last integral boundaries are from 0 to -1 and I always see them written from the smaller to the bigger number, aka from -1 to 0.
Does this makes a the result different? (maybe it's a mistake in the printing?)

Thanks.


attached image is another question, sorry for the unprofessional editing, it's from the book and it's not in English so i had to edit it a little... the pen markings are my own, what I think are correct/incorrect.
So I basically think statements 2 and 3 are correct, therefore answer D would be my choice, what do you think?

I need to send this out today and have total of 18 problems to answer (luckily this time they are multiple choices, not "open ended")
I would probably add more pictures as it's much easier and faster than typing the whole equations in the forum...

Thanks.

Originally Posted by ryu1

Given
and
the value of
is:

and

SO?

Originally Posted by Plato

and

SO?

so it's E. b-a



z+b=a
z=a-b
-z=b-a

right?

Originally Posted by ryu1

so it's E. b-a



z+b=a
z=a-b
-z=b-a

right?

Correct!

Originally Posted by Plato

Correct!

Thank you very much!

What you think about the problem in the picture?

Thanks.

Hello, ryu1!

Attached image is another question.
So I basically think statements 2 and 3 are correct.
Therefore, answer D would be my choice. .What do you think? . I agree!

Code:

      |
      *
      |   *
      |   |::*
      |   |::::*      4 
    --+---+------*----+----
      |   1      3*:::|
      |             *:|
      |               *

The graph of is continuous and passes through
= shaded area.
is the antiderivative of






Which are the correct statements?

Statement 1 is incorrect.
The integral from 1 to 4 is not the shaded area.
It is the net area (some of which is negative).

Statement 4 is equivalent to statement 1.
It is also incorrect.

Statement 2 is correct.
It gives the value of the definite integral.


Statement 3 is correct.
The total shaded area is the integral from 1 to 3
. . minus the integral from 3 to 4.

Originally Posted by Soroban

Hello, ryu1!



Statement 1 is incorrect.
The integral from 1 to 4 is not the shaded area.
It is the net area (some of which is negative).

Statement 4 is equivalent to statement 1.
It is also incorrect.

Statement 2 is correct.
It gives the value of the definite integral.


Statement 3 is correct.
The total shaded area is the integral from 1 to 3
. . minus the integral from 3 to 4.

Thank you.

New problem:
Given the function , R is a constant.

Find the anti derivative F(x) that such that F(R) = 0.

What is the value of F(0.5R)+F(2R)+F'(0.5R)+F'(2R)?

Answers:


I tend to go with C because I somehow got to 3/2R after calculating only the F'(0.5R)+F'(2R) (these are just the given function right?)
But I have a feeling the F(0.5R)+F(2R) will change it to something else...also where does the 0.19 comes from I wonder.

Thanks