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Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2) = -1

Is this true or false. I think it's false, but can someone explain to me why it's false.

The question is done correctly.

When you differentiate
-x^-1 you get x^-2
and all the arithmetic was done correctly.

If this an "area between curves" type, I have seen this before.
The function f(x) = 1/x^2 is discontinuous at x=0
so even though calculation-wise we come up with the answer above, it would be meaningless.

The answer is wrong because function x^(-2)>0 on [-2,2] except x=0 =>integral>0
This is Improper integral which is divergent.

x^(-1)-->infinity if x-->0

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Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2 = -1 Is this true or false. I think it's …
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consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …
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single_question_with_answer

the text passage contains a mathematical question and an answer to that question. the question is about evaluating the integral of x^-2 from -2 to 2, and the answer provided explains why the result is -1, but also points out that the answer is incorrect due to the discontinuity of the function at x=0. the passage further explains that the integral is improper and divergent because the function x^(-2) is always positive on the interval [-2,2] except at x=0, where it is undefined, and the integral should be greater than 0.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
posted by .

Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2) = -1

Is this true or false. I think it's false, but can someone explain to me why it's false.

The question is done correctly.

When you differentiate
-x^-1 you get x^-2
and all the arithmetic was done correctly.

If this an "area between curves" type, I have seen this before.
The function f(x) = 1/x^2 is discontinuous at x=0
so even though calculation-wise we come up with the answer above, it would be meaningless.

The answer is wrong because function x^(-2)>0 on [-2,2] except x=0 =>integral>0
This is Improper integral which is divergent.

x^(-1)-->infinity if x-->0

## Similar Questions

1. ### calculus

the integral sign where 4 is on top and 2 is at the bottom (x/2 + 3)dx and im trying to find the areas to evaluate the intrgral
2. ### calculus

Use Fundemental Theorem of Calculus part 1 to find the derivatives of the following: (i) F(x)=Integral ( top3, bottom x) e^-t^2 dt (ii) G(theta)=Integral ( top cos theta, bottom sin theta) 1/1-x^2 dx
3. ### Calculus

Evaluate the integral. -2 at the bottom of the integral sign and 7 at the top. f(x)dx f(x)={x if x<1 and 1/x if x> or equal to 1 I'm not sure how you would apply these two concepts together?
4. ### University calculus

if g(x)=the integral sign (with sin(x^2) on top and 10 at bottom) (1+t) dt, find g'(sqr root pie/2)
5. ### double integral

1. Sketch the region of integration & reverse the order of integration. Double integral y dydz... 1st (top=1, bottom =0)... 2nd(inner) integral (top=cos(piex), bottom=(x-2)... 2. Evaluate the integral by reversing the order of integration. …
6. ### Calculus

Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2 = -1 Is this true or false. I think it's …
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consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …
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consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …
9. ### calculus (please with steps and explanations)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …
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Hello, I'd appreciate any help with the following question below: Information: g(x)= 4 (x+1)^(-2/3) f(x)= ∫ g(t) dt The Question: What is f(26) ?

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user
TYPE: SINGLE_QUESTION_WITH_ANSWER

The text passage contains a mathematical question and an answer to that question. The question is about evaluating the integral of x^-2 from -2 to 2, and the answer provided explains why the result is -1, but also points out that the answer is incorrect due to the discontinuity of the function at x=0. The passage further explains that the integral is improper and divergent because the function x^(-2) is always positive on the interval [-2,2] except at x=0, where it is undefined, and the integral should be greater than 0.