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(x + 8 dx csc 4

EXAMPLE 2
Maximizing the Area Enclosed by a Fence
A farmer has 2000 yards of fence to enclose a rect...

Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the ve...

What are the formulas for the conversion of cylindrical to rectangular coordinates?

Derivatives using differentiation formula

Find the equation of the line.
Line of slope 6 through (9, 1)

In the given question as follows, find a function f that has the derivative f '(x) and whose graph p...

Consider the following relationship:
(x"A)~|
= BC
where A is a 2x3 matrix, B is a 3x3 matrix and C i...

Find the exact value of the six trigonometric functions of the angle θ in each figure.

(-1)"(2-5-8.(3n+2))(x-1)2n+2
3n. (n2 +1)
The derivative of the power series f(x) = 2
%3D
is
n=0
f(x)...

Write the following expression as a sum or difference of logarithms with no exponents. Simplify your...

Consider the function f(x)
26
Let F(x) be the antiderivative of f(x) with F(1) = 0.
Then F(x) =

In Problem ,find the slope and y-intercept of each line.Graph the line.                   y=-1

- The devil's curve (Gabriel Cramer, 1750) Find the slopes of
the devil's curve y* - 4y? - x* - 9 at...

Construct a table of values to investigate the following limits: (4 values from the left, 4 values f...

Atmospheric pressure decays exponentially as altitude increases. With pressure, P, in inches of merc...

Calculate the indefinite integral
t3 – 712 – t+43
dx.
– 7t2
t2 – 4t – 12

let v = (1, 3, −2) and w = (2, −1, 4).
 Compute the angle between v and w

a) An exponential model y = a · bª passes through the points (0, 7) and (2, 112). What are the value...

9-12. Verifying general solutions Verify that the given function y is a
solution of the differential...

Use the Half-angle Formulas to find the exact value of each expression.
tan 9π/ 8

ther the following improper integral converges or diverges. If it
its value.
1/5
x° In(5x)dx.
1
1000...

Let S be the upper surface of the sphere x- 2x+y+z = 0 and let r be the boundary.
Find [.curi(F) - a...

1. In a rectangular coordinate system, the point where the x- and y-axes meet is called the

Sketch the curve r = 1/2 θ (the spiral of Archimedes) for θ between 0 and 2π by plotting the points ...

Establish each identity given in attachment.

(-1)"n2n+1
n=0 32n-1(2n+ 1)!
The sum of the series
is
3
18
O 9/3
1
18
tan()
3
9 tan
Click Save and S...

Solve the following system of equations:
х + 2х> — хз — 2х4 3D 4
х1 + х2 — 2х3 — 4х4 %3D 10
2x1 + x2...

An airplane flying 390 feet per second at an altitude of 5000 feet flew directly over an observer. T...

In Problem,find zw and z/w Leave your answers in polar form.

Let f(x) = x4 – 8a² + 2.
Let m be the absolute minimum of f on [1,3].
Let M be the absolute maximum ...

Find the time required for an investment of 4700 dollars to grow to 6600 dollars at a continuous int...

Write a set of parametric equations for each of the following graphs.
11.
12.

5. А
to an equation in the variables x and y is an ordered pair (x, y) that makes the equation a tru...

Determine whether the following improper integral converges or diverges. If it
converges, find its v...

Find the slope of the graph of the function at the given point.

The function y
x- + ax +E6 has zeros at x = -5 and x = 6.
||
Determine a and b exactly and enter the...

(d) Determine the values of x on (−4, 4) for which f(x) is not continuous.(e) Determine the values o...

In Exercises 79-80, use a vertical shift to graph one period of the
function.
79. y = sin 2x + 1
80....

Given that the graph of f(x) passes through the point (2, 4) and that the slope of its tangent line ...

Use a computer algebra system to calculate the total length to two decimal places
r = √θ, 0 ≤ θ ≤ 4π

Find both the vector equation and the parametric equations of the line through (0,0,4) in the direct...

Factor the following polynomials. (a) x2 - 6x + 9 (b) x2 - 25 (c) 3x2 - 21x + 30 (d) 20 + 8x - x2

Using Basic Integration Rules :- , use the basic integration rules to find or evaluate the integral ?see the  equation as attached here :-

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="bold">&#8747;</mo><mi mathvariant="bold-italic">c</mi><mi mathvariant="bold-italic">s</mi><msup><mi mathvariant="bold-italic">c</mi><mn mathvariant="bold">2</mn></msup><mstyle mathvariant="bold"><mrow><mo>(</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mn>8</mn></mfrac><mo>)</mo></mrow></mstyle><mo mathvariant="bold">&#160;</mo><mi mathvariant="bold-italic">d</mi><mi mathvariant="bold-italic">x</mi></math>

The value of the integral:=?

Applying u-substitution rule:
                        Put :
                                         <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">u</mi><mo mathvariant="bold">=</mo><mi mathvariant="bold-italic">x</mi><mo mathvariant="bold">+</mo><mn mathvariant="bold">4</mn><mspace linebreak="newline"></mspace><mi mathvariant="bold-italic">d</mi><mi mathvariant="bold-italic">u</mi><mo mathvariant="bold">=</mo><mi mathvariant="bold-italic">d</mi><mi mathvariant="bold-italic">x</mi></math>
 
Hence,
                Substituting:
                                          <math xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="bold">∫</mo><mi mathvariant="bold-italic">c</mi><mi mathvariant="bold-italic">s</mi><msup><mi mathvariant="bold-italic">c</mi><mn mathvariant="bold">2</mn></msup><mrow><mo mathvariant="bold">(</mo><mfrac><mrow><mi mathvariant="bold">x</mi><mo mathvariant="bold">+</mo><mn mathvariant="bold">4</mn></mrow><mn mathvariant="bold">8</mn></mfrac><mo mathvariant="bold">)</mo></mrow><mo mathvariant="bold"> </mo><mi mathvariant="bold-italic">d</mi><mi mathvariant="bold-italic">x</mi><mspace linebreak="newline"></mspace><mo mathvariant="bold">=</mo><mo mathvariant="bold">∫</mo><mi mathvariant="bold-italic">c</mi><mi mathvariant="bold-italic">s</mi><msup><mi mathvariant="bold-italic">c</mi><mn mathvariant="bold">2</mn></msup><mstyle><mrow><mo>(</mo><mfrac><mi>u</mi><mn>8</mn></mfrac><mo>)</mo></mrow></mstyle><mo mathvariant="bold"> </mo><mi mathvariant="bold-italic">d</mi><mi mathvariant="bold-italic">u</mi><mspace linebreak="newline"></mspace></math>...

Calculus

Math

Using Basic Integration Rules :- , use the basic integration rules to find or evaluate the integral ?
see the  equation as attached here :-

(x + 8 dx csc 4

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(x + 8 dx csc 4

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