text: 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
  
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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 …
  7. ### Calculus (urgent help)
  
  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: …
  8. ### calculus
  
  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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explanation: The text extract contains a math question and an answer to this question. The question is about evaluating an integral, specifically the integral of x^-2 from -2 to 2. The answer provided explains why the result of the integral is -1, but then it is stated that the answer is actually wrong because the function x^(-2) is discontinuous at x=0, making the integral divergent.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 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 …
  7. ### Calculus (urgent help)
  
  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: …
  8. ### calculus
  
  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: …
  10. ### Calculus
  
  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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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract contains a math question and an answer to this question. The question is about evaluating an integral, specifically the integral of x^-2 from -2 to 2. The answer provided explains why the result of the integral is -1, but then it is stated that the answer is actually wrong because the function x^(-2) is discontinuous at x=0, making the integral divergent. 
  
  Label: question-and-answer