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One or more of the alternatives are correct.  Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up.

Which of the following improper integrals is (are) convergent?

  1. $\int ^{1} _{0} \frac{\sin x}{1-\cos x}dx$
  2. $\int ^{\infty} _{0} \frac{\cos x}{1+x} dx$
  3. $\int ^{\infty} _{0} \frac{x}{1+x^2} dx$
  4. $\int ^{1} _{0} \frac{1-\cos x}{\frac{x^5}{2}} dx$
in Calculus by Veteran (52.1k points) | 407 views
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someone please answer this question
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out of syllabus now
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So does that mean divergence and convergence is no longer in syllabus?
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most probably yes. i think we should concentrate only on last 5-6 yrs papers for next yrs pattern
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Here $A),C)$ and $D)$ converges and $B)$ and  diverges.

Because $A),D)$ are definite integral and going to a particular value. So, converges.

Diagram for $C)$ https://www.desmos.com/calculator/ucekshhehy

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Ma'am convergence and divergence is totally different topic in integration. Can we expect questions on them?
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May come for 1 marks.

First we need to do integration , and next check if it converges or diverges , right??
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So @srestha

if the answer is definite then it converges...

and for divergence ?

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