$5-10=$ Sketch the region enclosed by the given curves. Decide

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$y=e^{x}, \quad y=x^{2}-1, \quad x=-1, \quad x=1$$

Aidan J.

Numerade Educator

Sketch the region enclosed by the given curves. Decide

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$

y=\sin x, y=x, \quad x=\pi / 2, \quad x=\pi

$$

Bailey B.

Numerade Educator

$5-10=$ Sketch the region enclosed by the given curves. Decide

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$y=(x-2)^{2}, \quad y=x$$

Bailey B.

Numerade Educator

$5-10=$ Sketch the region enclosed by the given curves. Decide

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$y=\sin x, \quad y=2 x / \pi, \quad x \geqslant 0$$

Bailey B.

Numerade Educator

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$x=1-v^{2} \quad x=v^{2}-1$$

Bailey B.

Numerade Educator

whether to integrate with respect to $x$ or $y .$ Draw a typical

approximating rectangle and label its height and width. Then

find the area of the region.

$$4 x+y^{2}=12, \quad x=y$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$y=12-x^{2}, \quad y=x^{2}-6$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=x^{2}, \quad y=4 x-x^{2}

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=e^{x}, \quad y=x e^{x}, \quad x=0

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=\cos x, \quad y=2-\cos x, \quad 0 \leqslant x \leqslant 2 \pi

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

x=2 y^{2}, \quad x=4+y^{2}

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

x=y^{4}, \quad y=\sqrt{2-x}, \quad y=0

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=\cos \pi x, \quad y=4 x^{2}-1

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=|x|, \quad y=x^{2}-2

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=1 / x, \quad y=x, \quad y=\frac{1}{4} x, \quad x>0

$$

Bailey B.

Numerade Educator

$11-20=$ Sketch the region enclosed by the given curves and

find its area.

$$

y=\frac{1}{4} x^{2}, \quad y=2 x^{2}, \quad x+y=3, \quad x \geqslant 0

$$

Bailey B.

Numerade Educator

Sketch the region that lies between the curves $y=\cos x$ and

$y=\sin 2 x$ and between $x=0$ and $x=\pi / 2 .$ Notice that the

region consists of two separate parts. Find the area of this

region.

Bailey B.

Numerade Educator

Graph the curves $y=x^{2}-x$ and $y=x^{3}-4 x^{2}+3 x$ on a

common screen and observe that the region between them

consists of two parts. Find the area of this region.

Bailey B.

Numerade Educator

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

$$

y=\frac{2}{1+x^{4}}, \quad y=x^{2}

$$

Bailey B.

Numerade Educator

$3-26=$ Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

$$y=e^{1-x^{2}}, \quad y=x^{4}$$

Bailey B.

Numerade Educator

$3-26=$ Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

$y=\tan ^{2} x, \quad y=\sqrt{x}$

Bailey B.

Numerade Educator

$3-26=$ Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

$$y=\cos x, \quad y=x+2 \sin ^{4} x$$

Bailey B.

Numerade Educator

Racing cars driven by Chris and Kelly are side by side at

the start of a race. The table shows the velocities of each car

(in miles per hour) during the first ten seconds of the race.

Use Simpson's Rule to estimate how much farther Kelly

travels than Chris does during the first ten seconds.

Lucía G.

Numerade Educator

Two cars, $A$ and $B,$ start side by side and accelerate from

rest. The figure shows the graphs of their velocity functions.

(a) Which car is ahead after one minute? Explain.

(b) What is the meaning of the area of the shaded region?

(c) Which car is ahead after two minutes? Explain.

(d) Estimate the time at which the cars are again side by side.

Bailey B.

Numerade Educator