Anonymous asked in Science & MathematicsMathematics · 8 months ago

Can someone help me with these integrals, I'm not getting the correct answer?

For the value from -infinity to infinity (for both). N is a positive constant.

1. ∫( |N/|x|| )^2 dx

2. ∫( |(N*sin(x)) / x^3| )^2 dx



My work

1. ∫( |N/|x|| )^2 dx = N^2 ∫1/x^2 dx = N^2 [-1/x] = N^2 (-1/infinity - (-1/-infinity)) = N^2*0 = 0 which doesn't seem right to make. 

2. ∫( |(N*sin(x)) / x^3| )^2 dx = N^2 ∫sin^2(x)/x^6 dx which I'm not sure of beyond that

2 Answers

  • Use an online integral calculator like symbolab

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  • rotchm
    Lv 7
    8 months ago

    Show your reasoning & steps here & we will show you where you erred. 


    N² ∫ 1/x² dx, fro -∞ to ∞. Note that this is an improper integral. So its evaluation depends on how you were taught (defined) to evaluate it. The problem with this improper integral is the x=0 point. What are you supposed to do? [ I let you think a little]. 

    Now for your second question. Is it too an improper integral? And for what reasonS ? [yes, reasonS]. 

    Hints (for both question): Integrating from 0 to 1 gives?


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