Questions about adding and subtracting definite integrals.

sharktato

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\(\displaystyle a.\, \)\(\displaystyle \displaystyle \int_0^1\, \)\(\displaystyle f(x)\, dx\, =\, 6\)

\(\displaystyle b.\, \)\(\displaystyle \displaystyle \int_0^2\, \)\(\displaystyle f(x)\, dx\, =\, 4\)

\(\displaystyle c.\, \)\(\displaystyle \displaystyle \int_2^5\, \)\(\displaystyle f(x)\, dx\, =\, 1\)

\(\displaystyle \mbox{Use the above in answering the following:}\)

\(\displaystyle 1.\, \)\(\displaystyle \displaystyle \int_1^2\, \)\(\displaystyle f(x)\, dx\)

This is the one where I got -2, which is correct.

\(\displaystyle 2.\, \)\(\displaystyle \displaystyle \int_1^5\, \)\(\displaystyle f(x)\, dx\)

This is the one I got wrong, with an answer of -1.

Thanks,

Sharktato
 
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\(\displaystyle a.\, \)\(\displaystyle \displaystyle \int_0^1\, \)\(\displaystyle f(x)\, dx\, =\, 6\)

\(\displaystyle b.\, \)\(\displaystyle \displaystyle \int_0^2\, \)\(\displaystyle f(x)\, dx\, =\, 4\)

\(\displaystyle c.\, \)\(\displaystyle \displaystyle \int_2^5\, \)\(\displaystyle f(x)\, dx\, =\, 1\)

\(\displaystyle \mbox{Use the above in answering the following:}\)

\(\displaystyle 1.\, \)\(\displaystyle \displaystyle \int_1^2\, \)\(\displaystyle f(x)\, dx\)

This is the one where I got -2, which is correct.

\(\displaystyle 2.\, \)\(\displaystyle \displaystyle \int_1^5\, \)\(\displaystyle f(x)\, dx\)

This is the one I got wrong, with an answer of -1.

Thanks,

Sharktato
Something seems strange here. What is the statement of the problem, exactly?
 
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The point of the questions is to find out the value of the integral from 1-5 using the given information.

For example, for the first question I had to find the value of the integral from 1-2. In order to do this, I had to subtract the integral of 0-1 (6) from the integral of 0-2 (4) as that would satisfy the bounds 1-2. This is how I got -2 as my answer.

For the second question I assumed that I would have to add the integral of 1-2 (which I found was -2) to the integral of 2-5 (which is 1) in order to get the bounds of 1-5. After doing this however, I got -1 which is the wrong answer.

Thanks,

Sharktato
 
Sorry about that. I'll just write it out then rather than using pictures.

Use this information for #1 & #2:

The integral from 0-1 of f(x)dx=6. The integral from 0-2 of f(x)dx=4 The integral from 2-5 of f(x)dx=1

1. The integral from 1-2 of f(x)dx. This is the one where I got -2 which is correct.

2. The integral from 1-5 of f(x)dx. This is the one I got wrong with an answer of -1.

Thanks,

Sharktato

Since you got the first problem correct, I'll focus on the second problem:

\(\displaystyle \displaystyle \int^{5}_{1}\:f(x)dx=F(5)-F(1)=?\)

I get the same answer you did, of -1. The real question, then is, what answer does your book/teacher say is correct?
 
My Teacher wouldn't give me the answer to the question. He told me to create a chart to find the answer but when I did that, I got the same result.
 
My Teacher wouldn't give me the answer to the question. He told me to create a chart to find the answer but when I did that, I got the same result.
Since the helper got the same answer as you have (by two methods now), I'm thinking that the instructor may be reading off the wrong line from the answer sheet...? :oops:
 
Since the helper got the same answer as you have (by two methods now), I'm thinking that the instructor may be reading off the wrong line from the answer sheet...? :oops:

Yeah I don't know how my instructor got that answer. It doesn't make any sense to me. I'll try and talk to him again.

Thanks to everyone for all the help. I really appreciate it.

Thanks again,

Sharktato
 
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