91Ó°ÊÓ

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. $$\int_{1}^{\infty} \frac{x}{4+x^{2}} d x$$

Find the integrals $$\int \theta^{2} \cos 3 \theta d \theta$$

Say which formula, if any, to apply from the table of integrals. Give the values of any constants. $$\int x^{2} \sin 2 x d x$$

Find the integrals Check your answers by differentiation. $$\int y\left(y^{2}+5\right)^{8} d y$$

Find the integrals $$\int \sin ^{2} \theta d \theta$$

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. $$\int_{-\infty}^{0} \frac{e^{x}}{1+e^{x}} d x$$

What, if anything, does the comparison tell us about the convergence of the integral? $$\int_{0}^{1} \frac{\sin ^{2} x}{\sqrt{x}} d x, \text { compare with } \frac{1}{\sqrt{x}}$$

Say which formula, if any, to apply from the table of integrals. Give the values of any constants. $$\int \frac{4 x-2}{x^{2}+9} d x$$

Compute MID(4) for the integral \(\int_{0}^{2} f(x) d x\) using the values in Table 7.8. $$\begin{array}{c|c|c|c|c|c|c} \hline x & 0 & 0.25 & 0.50 & 0.75 & 1.00 & 1.25 \\ \hline f(x) & 2.3 & 5.8 & 7.8 & 9.3 & 10.3 & 10.8 \\ \hline x & 1.50 & 1.75 & 2.00 & 2.25 & 2.50 & 2.75 \\ \hline f(x) & 10.8 & 10.3 & 9.3 & 7.8 & 5.8 & 3.3 \\ \hline \end{array}$$

Find the integrals Check your answers by differentiation. $$\int x^{2}\left(1+2 x^{3}\right)^{2} d x$$