91Ó°ÊÓ

Evaluate. Assume \(u>0\) when ln u appears. $$\int \frac{e^{1 / t}}{t^{2}} d t$$

Distance and speed. A car accelerates at a constant rate from 0 mph to 60 mph in 30 sec. a) How fast is it traveling after 30 sec? b) How far has it traveled after 30 sec?

Distance and speed. A bicyclist decelerates at a constant rate from \(30 \mathrm{km} / \mathrm{hr}\) to a standstill in \(45 \mathrm{sec}\). a) How fast is the bicyclist traveling after \(20 \mathrm{sec} ?\) b) How far has the bicyclist traveled after \(45 \mathrm{sec} ?\)

Evaluate. Each of the following can be determined using the rules developed in this section, but some algebra may be required beforehand. $$\int(3 x-5)(2 x+1)^{2} d x$$

Evaluate. Assume \(u>0\) when ln u appears. $$\int\left(e^{t}+2\right) e^{t} d t$$

Distance and speed. A cheetah decelerates at a constant rate from \(50 \mathrm{km} / \mathrm{hr}\) to a complete stop in \(20 \mathrm{sec}\). a) How fast is the chectah moving after 10 sec? b) How far has the cheetah traveled after \(20 \mathrm{sec} ?\)

Evaluate. Each of the following can be determined using the rules developed in this section, but some algebra may be required beforehand. $$\int \sqrt[3]{64 x^{4}} d x$$

Evaluate. Assume \(u>0\) when ln u appears. $$\int \frac{d x}{x(\ln x)^{4}}$$

Evaluate. Assume \(u>0\) when ln u appears. $$\int \frac{t^{2}}{\sqrt[4]{2+t^{3}}} d t$$

Distance. For a freely falling object, \(a(t)=-32 \mathrm{ft} / \mathrm{sec}^{2}\) \(v(0)=\) initial velocity \(=v_{0}(\text { in } \mathrm{ft} / \mathrm{sec}),\) and \(s(0)=\) initial height \(=s_{0}(\text { in }[t) .\) Find a general expression \(\operatorname{lor} s(t)\) in terms of \(v_{0}\) and \(s_{0}\)