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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 recategorized by
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8 Comments

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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edited by
most probably yes. i think we should concentrate only on last 5-6 yrs papers for next yrs pattern
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edited by

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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