Applications of Integration

A certain object moves in such a way that its velocity (in $\mathrm{m} / \mathrm{s}$ ) after time $\mathrm{t}$ (in $\mathrm{s}$ ) is given by $v=t^{2}+2 t+10$. Use integration to find the distance traveled during the first four seconds. Answer:

Assume the annual rate of change in the national debt of a country (in billions of dollars per year) can be modeled by the function \[ D^{\prime}(t)=850.29+822.46 t-190.62 t^{2}+16.4 t^{3} \] where $t$ is the number of years since 1995. By how much did the debt increase between 1996 and 2006 ? The debt increased by $\$$ billion. (Round to two decimal places as needed.)

A company determined that the marginal cost, $C^{\prime}(x)$ of producing the $x$ th unit of a product is given by $C^{\prime}(x)=x^{3}-2 x$. Find the total cost function $C$, assuming that $C(x)$ is in dollars and that fixed costs are $\$ 8000$. \[ C(x)= \]

Find the area of the region enclosed by the curves $y=9 \sin x$ and $y=\sin (9 x), 0 \leq x \leq \pi$. The area of the region enclosed by the curves is (Simplify your answer.)

Let $\mathrm{R}$ be the region bounded by the following curves. Find the volume of the solid generated when $\mathrm{R}$ is revolved about the $x$-axis. Recall that $\cos ^{2} x=\frac{1}{2}(1+\cos 2 x)$. \[ y=\cos 2 x, y=0, x=0 \] The volume of the region revolved about the $x$-axis is cubic units. (Type an exact answer.)

Score: $26.5 / 30 \quad 23 / 25$ answered Question 25 『0/1 pt $2 \rightleftarrows 96$ (i) Details You are memorizing words for a vocabulary test. You studied a few days ago, and you know 23 word already. It is the night before the test, and you sit down to finish studying the words. Suppose that the rate of memorizing is given by $M^{\prime}(t)=-0.003 t^{2}+0.4 t$, where $M^{\prime}(t)$ is the memory rate, in words per minute. How many words are memorized in the first 14 minutes? words Round your answer to the nearest whole word Submit Question

Find the Root Mean Square of the function f(x) = 2x+3 on the interval [1, 4].