91Ó°ÊÓ

Digestion time of food is exponentially distributed with a mean of 1 hour. What is the probability that the food is digested in less than 30 minutes?

The integrals in Exercises \(1-40\) are in no particular order. Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$ \int(\csc x-\sec x)(\sin x+\cos x) d x $$

Evaluate the integrals in Exercises \(23-32\) $$ \int_{5 \pi / 6}^{\pi} \frac{\cos ^{4} x}{\sqrt{1-\sin x}} d x $$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. \(\int \sin ^{-1} \sqrt{x} d x\)

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. \(\int \frac{\cos ^{-1} \sqrt{x}}{\sqrt{x}} d x\)

The integrals in Exercises \(1-40\) are in no particular order. Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$ \int 3 \sinh \left(\frac{x}{2}+\ln 5\right) d x $$

Evaluate the integrals in Exercise \(25-30\) by using a substitution prior to integration by parts. $$ \int z(\ln z)^{2} d z $$

The integrals converge. Evaluate the integrals without using tables. $$\int_{2}^{4} \frac{d t}{t \sqrt{t^{2}-4}}$$

Use any method to evaluate the integrals. Most will require trigonometric substitutions, but some can be evaluated by other methods. $$\int \frac{6 d t}{\left(9 t^{2}+1\right)^{2}}$$

Pollinating flowers A biologist models the time in minutes until a bee arrives at a flowering plant with an exponential distribution having a mean of 4 minutes. If 1000 flowers are in a field, how many can be expected to be pollinated within 5 minutes?