Question 1

Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of $y=36-x^{2}, y=36$ and $x=6$ about the y-axis.

Accepted Answer

A)  $648$ $\pi$ 
B)  $144$ $\pi$ 
C)  $864$ $\pi$ 
D)  $108$ $\pi$ 
A)  $648$ $\pi$ 
B)  $144$ $\pi$ 
C)  $864$ $\pi$ 
D)  $108$ $\pi$

Question 2

Find the arc length of the graph of the given equation on the specified interval. y = $\frac{2}{3}$ ( $x^{2}$ + 1) $3 / 2$  
, [2, 5]

Accepted Answer

A)  $81$ 
B)  $\frac{243}{2}$ 
C)  $\frac{81}{2}$ 
D)  $\frac{243}{4}$ 
A)  $81$ 
B)  $\frac{243}{2}$ 
C)  $\frac{81}{2}$ 
D)  $\frac{243}{4}$

Question 3

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.)   (ft)

Accepted Answer

Question 4

Find the centroid of the region bounded by the graphs of $y=\sqrt{4-x^{2}}$ and $y=2-x$ .

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 5

Find the centroid of the region bounded by the graphs of $y=\sqrt{9-x^{2}}$ and $y=3-x$ .

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 6

Find the length of the curve for the interval $a \leq t \leq b$ . $y=\ln \left(\frac{e^{t}+1}{e^{t}-1}\right)$

Accepted Answer

The answer of Find the length of the curve for...

Question 7

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of $y=36-x^{2}, y=36$ and $x=6$ about the y-axis.

Find the arc length of the graph of the given equation on the specified interval. y = $\frac{2}{3}$ ( $x^{2}$ + 1) $3 / 2$ , [2, 5]

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft)

Find the centroid of the region bounded by the graphs of $y=\sqrt{4-x^{2}}$ and $y=2-x$ .

Find the centroid of the region bounded by the graphs of $y=\sqrt{9-x^{2}}$ and $y=3-x$ .

Find the length of the curve for the interval $a \leq t \leq b$ . $y=\ln \left(\frac{e^{t}+1}{e^{t}-1}\right)$

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 8: Further Applications of Integration

Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of y=36−x2,y=36y=36-x^{2}, y=36y=36−x2,y=36 and x=6x=6x=6 about the y-axis.

Find the arc length of the graph of the given equation on the specified interval. y = 23\frac{2}{3}32​ ( x2x^{2}x2 + 1) 3/23 / 23/2 , [2, 5]

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) (ft)

Find the centroid of the region bounded by the graphs of y=4−x2y=\sqrt{4-x^{2}}y=4−x2​ and y=2−xy=2-xy=2−x .

Find the centroid of the region bounded by the graphs of y=9−x2y=\sqrt{9-x^{2}}y=9−x2​ and y=3−xy=3-xy=3−x .

Find the length of the curve for the interval a≤t≤ba \leq t \leq ba≤t≤b . y=ln⁡(et+1et−1)y=\ln \left(\frac{e^{t}+1}{e^{t}-1}\right)y=ln(et−1et+1​)

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of $y=36-x^{2}, y=36$ and $x=6$ about the y-axis.

Find the arc length of the graph of the given equation on the specified interval. y = $\frac{2}{3}$ ( $x^{2}$ + 1) $3 / 2$ , [2, 5]

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft)

Find the centroid of the region bounded by the graphs of $y=\sqrt{4-x^{2}}$ and $y=2-x$ .

Find the centroid of the region bounded by the graphs of $y=\sqrt{9-x^{2}}$ and $y=3-x$ .

Find the length of the curve for the interval $a \leq t \leq b$ . $y=\ln \left(\frac{e^{t}+1}{e^{t}-1}\right)$

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)