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(Solved): 4. Check the convergence and divergence of the improper integrals by using Comparison Theorem (a) ...
4. Check the convergence and divergence of the improper integrals by using Comparison Theorem (a) \( \int_{1}^{\infty} \frac{\cos ^{2} x}{1+x^{2}} d x \) (c) \( \int_{0}^{\pi / 2} \frac{d x}{x \sin x} \) (b) \( \int_{1}^{\infty} \frac{2+e^{-x}}{x} d x \) (d) \( \int_{1}^{\infty} \frac{x}{\sqrt{1+x^{6}}} d x \)
Expert Answer
To check the convergence or divergence of the improper integrals, we can use the Comparison Theorem, which states that if there exist constants M and