Question 1

Express the limit as a definite integral on the given interval. $\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(3 r_{i} \sin r_{i}\right) \Delta r$  $\quad \quad [3,11]$

Accepted Answer

The answer of Express the limit as a definite integral...

Question 2

Evaluate $\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d t$

Accepted Answer

A)  $e^{\arccos x}$ 
B)  $e^{\arccos t}$ 
C)  $x$ 
D)  $e^{x}-\arccos x$ 
E)  $e^{\operatorname{arccost} \frac{x}{4}}$ 
A)  $e^{\arccos x}$ 
B)  $e^{\arccos t}$ 
C)  $x$ 
D)  $e^{x}-\arccos x$ 
E)  $e^{\operatorname{arccost} \frac{x}{4}}$

Question 3

The marginal cost of manufacturing x yards of a certain fabric is $C^{\prime}(x)=3-0.01 x+0.000006 x^{2}$ in dollars per yard. Find the increase in cost if the production level is raised from $2500$ yards to $6500$ yards.

Accepted Answer

A)  $\$ 278,000.00$ 
B)  $\$ 248,000.00$ 
C)  $\$ 268,000.00$ 
D)  $\$ 288,000.00$ 
E)  $\$ 258,000.00$ 
A)  $\$ 278,000.00$ 
B)  $\$ 248,000.00$ 
C)  $\$ 268,000.00$ 
D)  $\$ 288,000.00$ 
E)  $\$ 258,000.00$

Question 4

Find the area of the region that lies under the given curve. Round the answer to three decimal places. $y=\sqrt{3 x+2}, \quad 0 \leq x \leq 1$

Accepted Answer

A)  $1.906$ 
B)  $2.356$ 
C)  $1.856$ 
D)  $2.006$ 
E)  $2.156$ 
A)  $1.906$ 
B)  $2.356$ 
C)  $1.856$ 
D)  $2.006$ 
E)  $2.156$

Question 5

Find a function $f(x)$ such that $5+\int_{a}^{x} \frac{f(t)}{t^{2}} d t=8 \sqrt{x}$ for x > 0 and some number 
a.

Accepted Answer

The answer of Find a function $f(x)$ such that \(5+\int_{a}^{x}...

Question 6

Find the derivative of the function. $F(x)=\int_{x}^{x^{2}} e^{t^{3}} d t$

Accepted Answer

The answer of Find the derivative of the function. \(F(x)=\int_{x}^{x^{2}}...

Question 7

The acceleration function (in m/ $S^{2}$ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. $a(t)=t+4, v(0)=5,0 \leq t \leq 10$

Accepted Answer

A)  $v(t)=\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 566 \frac{2}{3} \mathrm{~m}$ 
B)  $v(t)=\frac{t^{2}}{2}+5 \mathrm{~m} / \mathrm{s}, 616 \frac{2}{3} \mathrm{~m}$ 
C)  $v(t)=\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 591 \frac{2}{3} \mathrm{~m}$ 
D)  $v(t)=\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 416 \frac{2}{3} \mathrm{~m}$ 
E)  $v(t)=\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 516 \frac{2}{3} \mathrm{~m}$ 
A)  $v(t)=\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 566 \frac{2}{3} \mathrm{~m}$ 
B)  $v(t)=\frac{t^{2}}{2}+5 \mathrm{~m} / \mathrm{s}, 616 \frac{2}{3} \mathrm{~m}$ 
C)  $v(t)=\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 591 \frac{2}{3} \mathrm{~m}$ 
D)  $v(t)=\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 416 \frac{2}{3} \mathrm{~m}$ 
E)  $v(t)=\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 516 \frac{2}{3} \mathrm{~m}$

Question 8

Use the Midpoint Rule with n = 10 to approximate the integral. $\int_{1}^{2} \sqrt{4+t^{2}} ~~d t$

Accepted Answer

A)  $7.510716$ 
B)  $1.510716$ 
C)  $12.510716$ 
D)  $2.510716$ 
E)  $10.510716$ 
A)  $7.510716$ 
B)  $1.510716$ 
C)  $12.510716$ 
D)  $2.510716$ 
E)  $10.510716$

Question 9

Evaluate the integral. $\int_{-2}^{5}\left|7 x-x^{2}\right| d x$ Round your answer to the nearest hundredth.

Accepted Answer

A)  $232.5$ 
B)  $64.5$ 
C)  $112.5$ 
D)  $62.5$ 
E)  $212.5$ 
A)  $232.5$ 
B)  $64.5$ 
C)  $112.5$ 
D)  $62.5$ 
E)  $212.5$

Question 10

Evaluate the integral if it exists. $\int_{0}^{1} 3 x^{2} \cos \left(x^{2}\right) d x$

Accepted Answer

A)  0 
B)  $2 \sin (2)$ 
C)  $\sin (3)$ 
D)  $\cos (2)$ 
E)  none of these 
A)  0 
B)  $2 \sin (2)$ 
C)  $\sin (3)$ 
D)  $\cos (2)$ 
E)  none of these

Express the limit as a definite integral on the given interval. $\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(3 r_{i} \sin r_{i}\right) \Delta r$ $\quad \quad [3,11]$

Evaluate $\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d t$

The marginal cost of manufacturing x yards of a certain fabric is $C^{\prime}(x)=3-0.01 x+0.000006 x^{2}$ in dollars per yard. Find the increase in cost if the production level is raised from $2500$ yards to $6500$ yards.

Find the area of the region that lies under the given curve. Round the answer to three decimal places. $y=\sqrt{3 x+2}, \quad 0 \leq x \leq 1$

Find a function $f(x)$ such that $5+\int_{a}^{x} \frac{f(t)}{t^{2}} d t=8 \sqrt{x}$ for x > 0 and some number a.

Find the derivative of the function. $F(x)=\int_{x}^{x^{2}} e^{t^{3}} d t$

The acceleration function (in m/ $S^{2}$ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. $a(t)=t+4, v(0)=5,0 \leq t \leq 10$

Use the Midpoint Rule with n = 10 to approximate the integral. $\int_{1}^{2} \sqrt{4+t^{2}} ~~d t$

Evaluate the integral. $\int_{-2}^{5}\left|7 x-x^{2}\right| d x$ Round your answer to the nearest hundredth.

Evaluate the integral if it exists. $\int_{0}^{1} 3 x^{2} \cos \left(x^{2}\right) d x$

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications 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 5: Applications of Integration

Express the limit as a definite integral on the given interval. lim⁡n→∞∑i=1n(3risin⁡ri)Δr\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(3 r_{i} \sin r_{i}\right) \Delta rlimn→∞​∑i=1n​(3ri​sinri​)Δr [3,11]\quad \quad [3,11][3,11]

Evaluate ddx∫0x(earccos⁡t)dt\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d tdxd​∫0x​(earccost)dt

The marginal cost of manufacturing x yards of a certain fabric is C′(x)=3−0.01x+0.000006x2C^{\prime}(x)=3-0.01 x+0.000006 x^{2}C′(x)=3−0.01x+0.000006x2 in dollars per yard. Find the increase in cost if the production level is raised from 250025002500 yards to 650065006500 yards.

Find the area of the region that lies under the given curve. Round the answer to three decimal places. y=3x+2,0≤x≤1y=\sqrt{3 x+2}, \quad 0 \leq x \leq 1y=3x+2​,0≤x≤1

Find a function f(x)f(x)f(x) such that 5+∫axf(t)t2dt=8x5+\int_{a}^{x} \frac{f(t)}{t^{2}} d t=8 \sqrt{x}5+∫ax​t2f(t)​dt=8x​ for x > 0 and some number a.

Find the derivative of the function. F(x)=∫xx2et3dtF(x)=\int_{x}^{x^{2}} e^{t^{3}} d tF(x)=∫xx2​et3dt

The acceleration function (in m/ S2S^{2}S2 ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. a(t)=t+4,v(0)=5,0≤t≤10a(t)=t+4, v(0)=5,0 \leq t \leq 10a(t)=t+4,v(0)=5,0≤t≤10

Use the Midpoint Rule with n = 10 to approximate the integral. ∫124+t2 dt\int_{1}^{2} \sqrt{4+t^{2}} ~~d t∫12​4+t2​ dt

Evaluate the integral. ∫−25∣7x−x2∣dx\int_{-2}^{5}\left|7 x-x^{2}\right| d x∫−25​​7x−x2​dx Round your answer to the nearest hundredth.

Evaluate the integral if it exists. ∫013x2cos⁡(x2)dx\int_{0}^{1} 3 x^{2} \cos \left(x^{2}\right) d x∫01​3x2cos(x2)dx

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications 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

Express the limit as a definite integral on the given interval. $\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(3 r_{i} \sin r_{i}\right) \Delta r$ $\quad \quad [3,11]$

Evaluate $\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d t$

The marginal cost of manufacturing x yards of a certain fabric is $C^{\prime}(x)=3-0.01 x+0.000006 x^{2}$ in dollars per yard. Find the increase in cost if the production level is raised from $2500$ yards to $6500$ yards.

Find the area of the region that lies under the given curve. Round the answer to three decimal places. $y=\sqrt{3 x+2}, \quad 0 \leq x \leq 1$

Find a function $f(x)$ such that $5+\int_{a}^{x} \frac{f(t)}{t^{2}} d t=8 \sqrt{x}$ for x > 0 and some number a.

Find the derivative of the function. $F(x)=\int_{x}^{x^{2}} e^{t^{3}} d t$

The acceleration function (in m/ $S^{2}$ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. $a(t)=t+4, v(0)=5,0 \leq t \leq 10$

Use the Midpoint Rule with n = 10 to approximate the integral. $\int_{1}^{2} \sqrt{4+t^{2}} ~~d t$

Evaluate the integral. $\int_{-2}^{5}\left|7 x-x^{2}\right| d x$ Round your answer to the nearest hundredth.

Evaluate the integral if it exists. $\int_{0}^{1} 3 x^{2} \cos \left(x^{2}\right) d x$