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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?

- $\int ^{1} _{0} \frac{\sin x}{1-\cos x}dx$
- $\int ^{\infty} _{0} \frac{\cos x}{1+x} dx$
- $\int ^{\infty} _{0} \frac{x}{1+x^2} dx$
- $\int ^{1} _{0} \frac{1-\cos x}{\frac{x^5}{2}} dx$

0

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

0

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

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