91Ó°ÊÓ

Use Table 7.9 $$\begin{array}{c|c|c|c|c|c} \hline t & 0.0 & 0.1 & 0.2 & 0.3 & 0.4 \\ \hline g(t) & 1.87 & 2.64 & 3.34 & 3.98 & 4.55 \\ \hline t & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\ \hline g(t) & 5.07 & 5.54 & 5.96 & 6.35 & 6.69 \\\ \hline \end{array}$$ Estimate \(\int_{0}^{0.9} g(t) d t\) using a right-hand sum with \(n=3.\)

Find the integrals $$\int(\ln t)^{2} d t$$

Antidifferentiate using the table of integrals. You may need to transform the integrand first. $$\int x^{5} \ln x d x$$

Find the integrals $$\int \ln \left(x^{2}\right) d x$$

Decide if the improper integral converges or diverges. $$\int_{1}^{\infty} \frac{d x}{x^{3}+1}$$

Calculate the integral if it converges. You may calculate the limit by appealing to the dominance of one function over another, or by l'Hopital's rule. $$\int_{0}^{\infty} \frac{z}{3+z^{2}} d z$$

Evaluate the integral.$$\int \frac{d x}{x^{3}-x^{2}} ; \text { use } \frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x-1}$$.

Find the integrals Check your answers by differentiation. $$\int x\left(x^{2}-4\right)^{7 / 2} d x$$

Antidifferentiate using the table of integrals. You may need to transform the integrand first. $$\int e^{-3 \theta} \cos \theta d \theta$$

Use Table 7.9 $$\begin{array}{c|c|c|c|c|c} \hline t & 0.0 & 0.1 & 0.2 & 0.3 & 0.4 \\ \hline g(t) & 1.87 & 2.64 & 3.34 & 3.98 & 4.55 \\ \hline t & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\ \hline g(t) & 5.07 & 5.54 & 5.96 & 6.35 & 6.69 \\\ \hline \end{array}$$ Estimate \(\int_{0}^{0.6} g(t) d t\) using the midpoint rule with \(n=\) 3.