91Ó°ÊÓ

The error formula for Simpson's rule depends on a. \(f(x)\) b. \(f^{\prime}(x)\) c. \(f^{(4)}(x)\) d. the number of steps

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{2}^{4} \frac{d x}{(x-3)^{2}} $$

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{0}^{\infty} \frac{1}{4+x^{2}} d x $$

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{0}^{2} \frac{1}{\sqrt{4-x^{2}}} d x $$

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{1}^{\infty} \frac{1}{x \ln x} d x $$

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{1}^{\infty} x e^{-x} d x $$

Evaluate the following integrals. If the integral is not convergent, answer "divergent." $$ \int_{-\infty}^{\infty} \frac{x}{x^{2}+1} d x $$

Without integrating, determine whether the integral \(\int_{1}^{\infty} \frac{1}{\sqrt{x^{3}+1}} d x\) converges or diverges by comparing the function \(f(x)=\frac{1}{\sqrt{x^{3}+1}}\) with \(g(x)=\frac{1}{\sqrt{x^{3}}}\).

Without integrating, determine whether the integral \(\int_{1}^{\infty} \frac{1}{\sqrt{x+1}} d x\) converges or diverges.

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{\infty} e^{-x} \cos x d x $$