Question 1

Solve the problem.
-(a) What area does the integral $\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }$ represent?
(b) Use a graphing utility to approximate the area to three decimal places.

Accepted Answer

The answer of Solve the problem.
-(a) What area does the...

Question 2

Solve the problem.
-$f ( x ) = \tan x$ is defined over the interval $\left[ 0 , \frac { 3 } { 2 } \right]$
(a) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 4 subintervals of equal length and choosing u as the left endpoint of each subinterval.
(b) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 8 subintervals of equal length and choosing $\mathrm { u }$ as the right endpoint of each subinterval.
(c) Express the area A as an integral.
(d) Use a graphing utility to approximate this integral to three decimal places.

Accepted Answer

The answer of Solve the problem.
-\(f ( x ) =...

Question 3

Solve the problem.
-$\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } + 1 }$ is defined on the interval $[ 0,4 ]$. In (a) and (b), approximate the area under $\mathrm { f }$ (to three decimal place follows:
(a) Partition $[ 0,4 ]$ into four subintervals of equal length and choose $u$ as the left endpoint of each subinterval.
(b) Partition $[ 0,4 ]$ into four subintervals of equal length and choose $\mathrm { u }$ as the right endpoint of each subinterval.
(c) Use a graphing utility to approximate the actual area $A$. s

Accepted Answer

The answer of Solve the problem.
-\(\mathrm { f } (...

Question 4

Solve the problem.
-$f ( x ) = \sqrt [ 3 ] { x }$ is defined on the interval 0, 6 .
(a) Approximate the area A under the graph of f by partitioning 0, 6 into three subintervals of equal length and
choose u as the left endpoint of each subinterval.
(b) Approximate the area A under the graph of f by partitioning 0, 6 into three subintervals of equal length and
choose u as the right endpoint of each subinterval.
(c) Express the area A as an integral.
(d) Use a graphing utility to approximate this integral to three decimal places.

Accepted Answer

The answer of Solve the problem.
-\(f ( x ) =...

Question 5

Solve the problem.
-What area does the integral $$\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$$ dx represent?
A) -1
B) 10
C) 11
D) 1

Accepted Answer

The answer of Solve the problem.
-What area does the integral...

Quiz 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Solve the problem. -(a) What area does the integral $\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }$ represent? (b) Use a graphing utility to approximate the area to three decimal places.

Solve the problem. -What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ dx represent?

Quiz 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Solve the problem. -(a) What area does the integral ∫0π/2sin⁡xcos⁡xdx\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }∫0π/2​sinxcosxdx represent? (b) Use a graphing utility to approximate the area to three decimal places.

Solve the problem. -What area does the integral ∫ln⁡6ln⁡5exdx\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x∫ln6ln5​exdx dx represent?

Solve the problem. -(a) What area does the integral $\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }$ represent? (b) Use a graphing utility to approximate the area to three decimal places.

Solve the problem. -What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ dx represent?