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study help
mathematics
calculus early transcendentals
Calculus Early Transcendentals 2nd edition William L. Briggs, Lyle Cochran, Bernard Gillett - Solutions
a. Evaluate using the substitution u = x + 1.b. Evaluate after first performing long division on the integrand.c. Reconcile the results in parts (a) and (b). х dx x + 1 x² dx x + 1
a. Evaluate ∫ cot x csc2 x dx using the substitution u = cot x.b. Evaluate ∫ cot x csc2 x dx using the substitution u = csc x.c. Reconcile the results in parts (a) and (b).
a. Evaluate ∫ tan x sec2 x dx using the substitution u = tan x.b. Evaluate ∫ tan x sec2 x dx using the substitution u = sec x.c. Reconcile the results in parts (a) and (b).
Use the approaches discussed in this section to evaluate the following integral. .2 ds s3 + 3s2 + 3s + 1
Use the approaches discussed in this section to evaluate the following integrals. 2 dx х? + 2х + 1
Use the approaches discussed in this section to evaluate the following integrals. -п/8 т/8 Vi - cos 4х dx
Use the approaches discussed in this section to evaluate the following integrals. et - dx e2x + 2e* + 1
Use the approaches discussed in this section to evaluate the following integrals. 8/- TT VI - сos 4х dx
Use the approaches discussed in this section to evaluate the following integrals. dx x2 + 6x + 13
Use the approaches discussed in this section to evaluate the following integrals. dp Г. 4 - Vp
Use the approaches discussed in this section to evaluate the following integrals. dx x!/2 + x³/2
Use the approaches discussed in this section to evaluate the following integrals. TT CT/2 Vi + cos 2.x dx
Use the approaches discussed in this section to evaluate the following integrals.∫ sin x sin 2x dx
Use the approaches discussed in this section to evaluate the following integrals. V1 + Vĩ dx
Use the approaches discussed in this section to evaluate the following integral. dx x² + 2x + 2
Use the approaches discussed in this section to evaluate the following integrals. 6° dx 1 - Vx 4
Determine whether the following statements are true and give an explanation or counter example.a.b. Long division simplifies the evaluation of the integral c. 3 dx = x + 4 3 dx + - dх. 4 .2 .3 x' + 2 dx. Зx + х .4
Evaluate the following integrals. do 1 - csc 0
Evaluate the following integrals. dx sec x – 1
Evaluate the following integrals. х dx х
Evaluate the following integrals. do 1 + sin 0
Evaluate the following integrals. dx x* + 2x2 + 1 4
Evaluate the following integrals. do V27 – 60 – 0²
Evaluate the following integrals. х dx x2 + 4x + 8
Evaluate the following integrals. dx х2 — 2х + 10 10
Evaluate the following integrals. 6 – x* X' dx x² + 4
Evaluate the following integrals. = dt t + 1
Evaluate the following integrals. x² + 2 dx
Evaluate the following integrals. x + 2 - dx x + 4
Evaluate the following integrals. Зх + 1 dx V4 — х2
Evaluate the following integrals. 2 — Зх dx V1 – x²
Evaluate the following integrals. 4 + e-2r dx Зх e3x
Evaluate the following integrals. sin t + tan t dt cos? t
Evaluate the following integrals. 5/2 1/2 dx х3/2 х
Evaluate the following integrals. x + 2 dx x² + 4
Evaluate the following integrals. dy -1 -3 У
Evaluate the following integrals. dx -1 х
Evaluate the following integrals. x(3x + 2) dx .2 Vx³ + x² + 4
Evaluate the following integrals. cost.x dx sin° x
Evaluate the following integrals. sin' x cos x
Evaluate the following integrals. *In°(x²) dx х
Evaluate the following integrals. ,2z e?z dz e2z – 4e
Evaluate the following integrals. et х dx e* – 2e*
Evaluate the following integrals. ,2Vy+1 dy Vy
Evaluate the following integrals. et dx e* + 1
Evaluate the following integrals. Го dх V4 - х
Evaluate the following integrals. In 2x dx
Evaluate the following integrals.∫ e3 - 4x dx
Evaluate the following integrals. .Зп/8 TT dx sin ( 2x 2x
Evaluate the following integrals.∫ (9x - 2)-3 dx
Evaluate the following integrals. dx (3 – 5x)4
Describe a first step in integrating x10 – 2x4 + 10x² + 1 dx. Зх3
Describe a first step in integrating 10 dx. 4х + 5 .2
Describe a first step in integrating .3 X* x³ – 2x + 4 dx.
What trigonometric identity is useful in evaluating ∫ sin2 x dx?
Before integrating, how would you rewrite the integrand of ∫ (x4 + 2)2 dx?
What change of variables would you use for the integral ∫ (4 - 7x)-6 dx?
Evaluate lim (tanh x)*. х
Find the linear approximation to f(x) = cosh x at a = ln 3 and then use it to approximate the value of cosh 1.
Find the area of the region bounded by the curves f(x) = 8 sech2 x and g(x) = cosh x.
Compute the following derivatives.a. d6/dx6(cosh x)b. d/dx(x sech x)
Let f(x) = ax2 + bx + c be an arbitrary quadratic function and choose two points x = p and x = q. Let L1 be the line tangent to the graph of f at the point (p, f(p)) and let L2 be the line tangent to the graph at the point (q, f (q)). Let x = s be the vertical line through the intersection point of
A commonly used distribution in probability and statistics is the log-normal distribution. (If the logarithm of a variable has a normal distribution, then the variable itself has a log-normal distribution.) The distribution function iswhere ln x has zero mean and standard deviation σ > 0.a.
Use the graphing techniques of Section 4.3 to graph the following functions on their domains. Identify local extreme points, inflection points, concavity, and end behavior. Use a graphing utility only to check your work.f(x) = ln x - ln2x
Use the graphing techniques of Section 4.3 to graph the following functions on their domains. Identify local extreme points, inflection points, concavity, and end behavior. Use a graphing utility only to check your work.f(x) = ex(x2 - x)
A savings account advertises an annual percentage yield (APY) of 5.4%, which means that the balance in the account increases at an annual growth rate of 5.4%/yr.a. Find the balance in the account for t ≥ 0 with an initial deposit of $1500, assuming the APY remains fixed and no additional deposits
Growing from an initial population of 150,000 at a constant annual growth rate of 4%/yr, how long will it take a city to reach a population of 1 million?
The mass of radioactive material in a sample has decreased by 30% since the decay began. Assuming a half-life of 1500 years, how long ago did the decay begin?
Evaluate the following integrals. dx р9 — х6
Evaluate the following integrals. х et dx + 4 Vezr ,2x
Evaluate the following integrals. dx Vx² – 9
Evaluate the following integrals. eIn 3 coth s ds In 2
Evaluate the following integrals. x + 4 dx x2 + 8x + 25
Evaluate the following integrals. 10V dx VI
Evaluate the following integrals. ев dx 2 x In x
Evaluate the following integrals. et dx 4e* + 6
Find the total force on the face of a semicircular dam with a radius of 20 m when its reservoir is full of water. The diameter of the semicircle is the top of the dam.
A cylindrical water tank has a height of 6 m and a radius of 4 m. How much work is required to empty the full tank by pumping the water to an outflow pipe at the top of the tank?
a. It takes 50 J of work to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m?b. It takes 50 N of force to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m?
Find the mass of the following thin bars.A bar on the interval 0 ≤ x ≤ 6 with a density if 0 < x < 2 p(x) = 2 if 2 < x < 4 4 if 4 < x < 6.
Find the mass of the following thin bars.A 3-m bar with a density (in g/m) of ρ(x) = 150e-x/3, for 0 ≤ x ≤ 3
Find the mass of the following thin bars.A bar on the interval 0 ≤ x ≤ 9 with a density (in g/cm) given by ρ(x) = 3 + 2√x.
Let and let R be the region bounded by the graph of f and the x-axis on the interval [1, 2].a. Find the area of the surface generated when the graph of f on [1, 2] is revolved about the x-axis.b. Find the length of the curve y = f(x) on [1, 2].c. Find the volume of the solid generated when R is
Find the surface area of a cone (excluding the base) with radius 4 and height 8 using integration and a surface area integral.
Let f(x) = √3x - x2 and let R be the region bounded by the graph of f and the x-axis on the interval [0, 3].a. Find the area of the surface generated when the graph of f on [0, 3] is revolved about the x-axis.b. Find the volume of the solid generated when R is revolved about the x-axis.
Let f(x) = 1/3 x3 and let R be the region bounded by the graph of f and the x-axis on the interval [0, 2].a. Find the area of the surface generated when the graph of f on [0, 2] is revolved about the x-axis.b. Find the volume of the solid generated when R is revolved about the y-axis.c. Find the
Find the length of the following curves.y = ln x between x = 1 and x = b > 1 given thatUse any means to approximate the value of b for which the curve has length 2. Vx² + a² - dx a + Vx² + a² + C. Vx? + a² – a In .2 х х
Find the length of the following curves.y = x3/3 + x2 + x + 1/(4x + 4) on the interval [0, 4]
Find the length of the following curves.y = x1/2 - x3/2/3 on the interval [1, 3]
Find the length of the following curves.y = x3/6 + 1/(2x) on the interval [1, 2]
Find the length of the following curves.y = cosh-1 x on the interval [√2, √5]
Find the length of the following curves.y = 2x + 4 on the interval [-2, 2] (Use calculus.)
Let R be the region bounded by the graph of f(x) = cx(1 - x) and the x-axis on [0, 1]. Find the positive value of c such that the volume of the solid generated by revolving R about the x-axis equals the volume of the solid generated by revolving R about the y-axis.
Determine the area of the region bounded by the curves x = y2 and x = (2 - y2)2 (see figure). УА х%3D (2 — у?)? x = y2 х
Let R be the region bounded by y = 1/xp and the x-axis on the interval [1, a], where p > 0 and a > 1 (see figure). Let Vx and Vy be the volumes of the solids generated when R is revolved about the x- and y-axes, respectively.a. With a = 2 and p = 1, which is greater, Vx or Vy?b. With a = 4
The region R is bounded by the curves x = y2 + 2, y = x - 4, and y = 0 (see figure).a. Write a single integral that gives the area of R.b. Write a single integral that gives the volume of the solid generated when R is revolved about the x-axis.c. Write a single integral that gives the volume of the
Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.The region bounded by the graphs of y = 2x, y = 6 - x, and y = 0 is revolved about the line y = -2 and the line x = -2. Find the volumes of the resulting solids. Which one is greater?
Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.The region bounded by the graphs of y = 6x and y = x2 + 5 is revolved about the line y = -1 and the line x = -1. Find the volumes of the resulting solids. Which one is greater?
Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.The region bounded by the graphs of y = (x - 2)2 and y = 4 is revolved about the line y = 4. What is the volume of the resulting solid?
Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.The region bounded by the graph of y = 4 - x2 and the x-axis on the interval [-2, 2] is revolved about the line x = -2. What is the volume of the solid that is generated?
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