AREA OF A BOUNDED REGION (CALCULATOR USAGE)

Authored by Greg Snelick

Mathematics

9th - 12th Grade

Used 10+ times

AREA OF A BOUNDED REGION (CALCULATOR USAGE)

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10 questions

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MULTIPLE CHOICE QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region Upper Curve

$y_1$

$y_2$

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region Lower Curve

$y_1$

$y_2$

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region
Points of Intersections
$x=A$ and $x=B$
Submit $A,B$ $\left(A<B\right)$

(a)

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Shade Command

$Shade\left(y_1,y_2\right)$

$Shade\left(y_2,y_1\right)$

MULTIPLE CHOICE QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region

$\int_0^{\ 4}\ \left(y_1-y_2\right)dx$

$\int_0^{\ 4}\ \left(y_2-y_1\right)dx$

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Difference of Two Areas
$A-\frac{B}{C}$
Submit $A,B,C$

(a)

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Exact Area of the Bounded Region
$\frac{A}{B}$
Submit $A,B$

(a)

MULTIPLE SELECT QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Check all that apply

$\int_0^{\ 4}\ \left(x^2-4x\right)dx$

$\int_0^{\ 4}\ \left(4x-x^2\right)dx$

$\int_4^{\ 0}\ \left(4x-x^2\right)dx$

$\int_4^{\ 0}\ \left(x^2-4x\right)dx$

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=2x$
Window $\left[-2,6,1\right]\ x\ \left[-2,12,2\right]$
Area of the Bounded Region
Difference of Two Areas
$A-\frac{B}{C}$
Submit $A,B,C$

(a)

10.

FILL IN THE BLANKS QUESTION

1 min • 2 pts

$y_1=x^2-4x+5\ \ ,\ \ y_2=2x$
Window $\left[-2,6,1\right]\ x\ \left[-2,12,2\right]$
Area of the Bounded Region
$\frac{A}{B}$
Submit $A,B$

(a)

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AREA OF A BOUNDED REGION (CALCULATOR USAGE)

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Bounded Region Upper Curve

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Bounded Region Lower Curve

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Bounded Region Points of Intersections x=Ax=Ax=A and x=Bx=Bx=B Submit A,BA,BA,B (A<B)\left(A<B\right)(A<B) (a)

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Area of the Bounded Region Shade Command

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Area of the Bounded Region

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Area of the Bounded Region Difference of Two Areas A−BCA-\frac{B}{C}A−CB​ Submit A,B,CA,B,CA,B,C (a)

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Exact Area of the Bounded Region AB\frac{A}{B}BA​ Submit A,BA,BA,B (a)

y1=x2−4x+5 , y2=5y_1=x^2-4x+5\ \ ,\ \ y_2=5y1​=x2−4x+5 , y2​=5 Window [−2,5,1] x [−2,6,2]\left[-2,5,1\right]\ x\ \left[-2,6,2\right][−2,5,1] x [−2,6,2] Area of the Bounded Region Check all that apply

y1=x2−4x+5 , y2=2xy_1=x^2-4x+5\ \ ,\ \ y_2=2xy1​=x2−4x+5 , y2​=2x Window [−2,6,1] x [−2,12,2]\left[-2,6,1\right]\ x\ \left[-2,12,2\right][−2,6,1] x [−2,12,2] Area of the Bounded Region Difference of Two Areas A−BCA-\frac{B}{C}A−CB​ Submit A,B,CA,B,CA,B,C (a)

y1=x2−4x+5 , y2=2xy_1=x^2-4x+5\ \ ,\ \ y_2=2xy1​=x2−4x+5 , y2​=2x Window [−2,6,1] x [−2,12,2]\left[-2,6,1\right]\ x\ \left[-2,12,2\right][−2,6,1] x [−2,12,2] Area of the Bounded Region AB\frac{A}{B}BA​ Submit A,BA,BA,B (a)

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$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region Upper Curve

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region Lower Curve

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Bounded Region
Points of Intersections
$x=A$ and $x=B$
Submit $A,B$ $\left(A<B\right)$

(a)

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Shade Command

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Difference of Two Areas
$A-\frac{B}{C}$
Submit $A,B,C$

(a)

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Exact Area of the Bounded Region
$\frac{A}{B}$
Submit $A,B$

(a)

$y_1=x^2-4x+5\ \ ,\ \ y_2=5$
Window $\left[-2,5,1\right]\ x\ \left[-2,6,2\right]$
Area of the Bounded Region
Check all that apply

$y_1=x^2-4x+5\ \ ,\ \ y_2=2x$
Window $\left[-2,6,1\right]\ x\ \left[-2,12,2\right]$
Area of the Bounded Region
Difference of Two Areas
$A-\frac{B}{C}$
Submit $A,B,C$

(a)

$y_1=x^2-4x+5\ \ ,\ \ y_2=2x$
Window $\left[-2,6,1\right]\ x\ \left[-2,12,2\right]$
Area of the Bounded Region
$\frac{A}{B}$
Submit $A,B$

(a)