91影视

In the following exercises, compute each integral using appropriate substitutions. \(\int \frac{e^{t}}{1+e^{2 t}} d t\)

Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow \pi} \frac{1+\cos x}{\sin x} $$

In the following exercises, integrate using the indicated substitution. $$ \int \ln (x) \frac{\sqrt{1-(\ln x)^{2}}}{x} d x ; u=\ln x $$

In the following exercises, compute each integral using appropriate substitutions. \(\int \frac{d t}{t \sqrt{1-\ln ^{2} t}}\)

In the following exercises, does the right-endpoint approximation overestimate or underestimate the exact area? Calculate the right endpoint estimate R50 and solve for the exact area. $$ \text { [T] } y=e^{x} \text { over }[0,1] $$

Find the area under \(y=1 / x\) and above the \(x\) -axis from \(x=1\) to \(x=4\) $$ \frac{d}{d x} \ln \left(x+\sqrt{x^{2}+1}\right)=\frac{1}{\sqrt{1+x^{2}}} $$

Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \text { [T] } \lim _{x \rightarrow 0}\left(\csc x-\frac{1}{x}\right) $$

In the following exercises, does the right-endpoint approximation overestimate or underestimate the exact area? Calculate the right endpoint estimate R50 and solve for the exact area. $$ y=e^{-x} \text { over }[0,1] $$

For the following exercises, find the antiderivatives for the functions.\(\int \frac{d x}{\sqrt{x^{2}+1}}\)

In the following exercises, compute each integral using appropriate substitutions. \(\int \frac{d t}{t\left(1+\ln ^{2} t\right)}\)