Explain why $u=a \sin \theta$ is a useful substitution when an integral contains an expression of the form $\sqrt{a^2-u^2}$.

Write the polar form of 1/x.

Add $-4 \angle 150^{\circ}+6 \angle-200^{\circ}$. Express the answer in polar form.

Find $4 \vec{v}_1-7 \vec{v}_2$ when $\vec{v}_1=\langle 2,2\rangle$ and $\vec{v}_2=\langle-1,3\rangle$.

Let $\vec{v}_1=(6,5\rangle$ and $\bar{v}_2=\langle-2,11\rangle$. Express $\bar{v}_1+\bar{v}_2$ in the form $\langle a, b\rangle$.

Find the general solution to the differential equation $y\left(x^2+1\right) \dfrac{d y}{d x}=x y^2$.

Integrate to obtain an exact answer.

$$\int 2 \sec ^3 x d x$$

Integrate to obtain an exact answer.

$$\int \frac{\sqrt{16-x^2}}{x^2} d x$$

The base of a solid is a circle of radius 4. Every vertical cross section of the solid perpendicular to the base and parallel to a given diameter is a rectangle whose height is half the length of its base. Find the volume of the solid.

Fill in each blank with the most appropriate word from Lesson 5.

I must learn to make backup copies of my computer documents: a power failure last night ______ my entire term paper from the computer!

Make a substitution to express the integrand as a rational function and then evaluate $\displaystyle\int_9^{16} \frac{\sqrt{x}}{x-4} d x$.

Writing Original Sentences Using Conjunctions. Use each conjunction below in an original sentence. Remember that you can connect nouns, verbs, adjectives, phrases, or sentences. and

Underline the word in parentheses that best completes each sentence.

Trevor's new job is (farther, further) from home than his old job.

Choose the correct word or expression from the list below.

-la capitale

• Je me souviens.

• l’Espagne

• métro, boulot, dodo

• Rennes

• les Marseillais

• les Parisiens

• la Belgique

• Comment s’appellent les habitants de Paris?