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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value.for any positive integer n. 1/n. f(x) = x/n; [0, 1],
Evaluate the following integrals using the Fundamental Theorem of Calculus. ⁹2 + Vt t 4 dt
Evaluate the following integrals using the Fundamental Theorem of Calculus. [ (x + √x) dx
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value.for any positive integer n. f(x) = x"; [0, 1],
Evaluate the following integrals using the Fundamental Theorem of Calculus. π/4 S™ 0 2 cos x dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. 2 [(x². -2 (x² - 4) dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 In 8 ex dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. S²x 0 x(x-2)(x-4) dx
Find the following integrals. X 3√x +4 dx
Find the following integrals. X Vx - 4 dx
Find the following integrals. y² (y + 1)4 S dy
Find the following integrals. ex et - ex ex + ex dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. (x-3-8) dx 1/2
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 7/4 sec- Ꮎ dᎾ
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 1/2 dx V1 - x²
Find the following integrals. [xV2x + 1dx √2x
Evaluate the following integrals using the Fundamental Theorem of Calculus. -2 x-3 dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. xp (+ - x)(x - 1) J
Evaluate the following integrals using the Fundamental Theorem of Calculus. ["a 0 (1 - sin x) dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. π/2 -π/2 (cos x - 1) dx
Find the following integrals. f(x. (x + 1)√3x + 2 dx
Use symmetry to evaluate the following integrals. π/4 tan x dx -π/4
Suppose that Evaluate the following integrals or state that there is not enough information. S₁f(x) dx = 6, ₁ g(x) dx = 4, and ƒ^ƒ(x) dx = 2.
Suppose that Evaluate the following integrals or state that there is not enough information. S₁f(x) dx = 6, ₁ g(x) dx = 4, and ƒ^ƒ(x) dx = 2.
Use symmetry to evaluate the following integrals. π/4 [ sec² x dx J-π/4
Use symmetry to evaluate the following integrals. 2 La (1 - |x|³) dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. 2 [²3/01 - dt
Use a change of variables to evaluate the following definite integrals. π/2 Jπ/4 COS X - dx sin² x
Evaluate the following integrals using the Fundamental Theorem of Calculus. 4 X Vx 43 dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 TT/8 cos 2x dx
Evaluate the following integrals using the Fundamental Theorem of Calculus. S 0 10e²x dx
Use symmetry to evaluate the following integrals. 3 - 4x -2x² + 1 -dx
Use a change of variables to evaluate the following definite integrals. 3 v² + 1 Vv³ + 3y + 4 3 dv
Use a change of variables to evaluate the following definite integrals. 2/5 [20(8 5) dx 2/(5√3) xV25x² - 1
Determine the area of the shaded region in the following figures. УА y = x x y=x²2²-2
Another description of the Gateway Arch iswhere the base of the arch is [-315, 315] and x and y are measured in feet. Find the average height of the arch above the ground. y = 1260 - 315(e0.00418x +
Determine the area of the shaded region in the following figures. y = 2t y = 3-x X
Sketch the following regions (if a figure is not given) and find the area.The region bounded by y = 8 - 2x, y = x + 8, and y = 0 (Use integration.) y = x + 8 0 y=8-2r X
Determine the area of the shaded region in the following figures. УА y = x³ y = x X
Determine the area of the shaded region in the following figures. YA 이 y = sec² x 4 y = 4 cos²x X
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = x, y = 2√x УА y = 2√x R y = x + X
Sketch the following regions (if a figure is not given) and find the area.The region bounded by y = ln x, y = 2, y = 0, and x = 0 УА y = 2 y = ln x X
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = x, y = √x УА O s y = √x y = x X
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = ex/², y = ex/², x = ln 2, x = In 3 YA y
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = |x|, y = 2x²
Describe how a solid of revolution is generated.
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = x, y = x + 2, x = 0, x = 4 YA y = x +
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = x + 3, y = x² + 1
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = Vsin x, y = 1, x = 0
Find the volume of the solid of revolution. Sketch the region in question.The region bounded byrevolved about the x-axis || y= 1 √x² + 1 and y= = 1 V2
Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis. y = sin x, y = Vsin x, for 0 ≤ x ≤ π/2
LetFind the volume of the solid formed when the region bounded by the graph of f , the x-axis, and the line x = 6 is revolved about the x-axis. f(x) = X 2x2 -2x +18 if 0 ≤ x ≤ 2 if 2 < x≤ 5 if
Sketch the following regions (if a figure is not given) and find the area.The region bounded by y = x and x = y2
Sketch the following regions (if a figure is not given) and find the area.The region bounded by y = ln x2, y = ln x, and x = e2
Find the area of the regions shown in the following figures. YA 이 y = 4V2T y=2x2 y = -4.x + 6 X
Find the area of the regions shown in the following figures. YA = 2x y = 1 - x2 지 X
Find the volume of the solid of revolution. Sketch the region in question.The region bounded by y = (ln x)/√x, y = 0, and x = 2 revolved about the x-axis
Find the area of the regions shown in the following figures. УА y = x² x = 2 sin² y X
Find the volume of the solid of revolution. Sketch the region in question.The region bounded by y = 1/√x, y = 0, x = 2, and x = 6 revolved about the x-axis
Find the volume of the solid of revolution. Sketch the region in question.The region bounded by y = ex, y = 0, x = 0, and x = 2 revolved about the x-axis
Find the volume of the solid of revolution. Sketch the region in question.The region bounded by y = ln x, y = ln x2, and y = ln 8 revolved about the y-axis
Find the volume of the solid of revolution. Sketch the region in question.The region bounded by y = e-x, y = 0, x = 0, and x = p > 0 revolved about the x-axis (Is the volume bounded as p → ∞?)
Find the area of the regions shown in the following figures. 0 X = (y-2)² 3 y = 8 - x X
If f is an even function, why is fa f(x) dx = 2 f₁ f(x) dx? -a
Use a calculator and right Riemann sums to approximate the area of the region described. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals.
Evaluate the following integrals using the Fundamental Theorem of Calculus. √√3 dx 1 + x²
Evaluate the following integrals using the Fundamental Theorem of Calculus. TT/8 TT/16 8 csc² 4x dx
Use the definition of the definite integral to evaluate the following definite integrals. Use right Riemann sums and Theorem 5.1.Data from in Theorem 5.1 1₁² (x²- 0 (x² - 1) dx
Use a change of variables to evaluate the following definite integrals. X 2 x² + 1 - dx
Suppose f is an even function and 8 f(x) dx = 18. a. Evaluate Prox f(x) dx b. Evaluate 8 x f(x) dx -8
Use the definition of the definite integral to evaluate the following definite integrals. Use right Riemann sums and Theorem 5.1.Data from in Theorem 5.1 [(x². (x² - 1) dx
Use a change of variables to evaluate the following definite integrals. 0 1/4 X V1-16x² Te dx
Use the definition of the definite integral to evaluate the following definite integrals. Use right Riemann sums and Theorem 5.1.Data from in Theorem 5.1 2 S 0 4x³ dx
Use a change of variables to evaluate the following definite integrals. 1/√3 1/3 4 9x² + 1 - dx
Prove that the integrand is either even or odd. Then give the value of the integral or show how it can be simplified. Assume that f and g are even functions and p and q are odd functions. a f(p(x))
Use a change of variables to evaluate the following definite integrals. 0 In 4 et 3 + 2ex dx
Use a calculator and right Riemann sums to approximate the area of the region described. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals.
Evaluate the following integrals. sin² 0 + TT 6 do
Prove that the integrand is either even or odd. Then give the value of the integral or show how it can be simplified. Assume that f and g are even functions and p and q are odd functions.
Prove that the integrand is either even or odd. Then give the value of the integral or show how it can be simplified. Assume that f and g are even functions and p and q are odd functions. a p(q(x))
Prove that the integrand is either even or odd. Then give the value of the integral or show how it can be simplified. Assume that f and g are even functions and p and q are odd functions. a p(g(x))
Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) = x² 25; [2, 4]
Use a calculator and right Riemann sums to approximate the area of the region described. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals.
Evaluate the following integrals. . 1 sin - dx x² X
Evaluate the following integrals. π/4 -π/4 sin² 20 de
Find the area of the region bounded by the graph of f and the x-axis on the given interval. _f(x) = x³ = 1; [-1,2]
Evaluate the following integrals. π/4 cos² 80 de
Evaluate the following integrals. (tan-¹ x)5 1 + x² - dx
Find the area of the region bounded by the graph of f and the x-axis on the given interval. 1 ƒ(x) = ½ [−2,−1] X
Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) = x(x + 1)(x - 2); [1,2]
Use a calculator and right Riemann sums to approximate the area of the region described. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals.
Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) = sin x; [-7/4, 3π/4]
Evaluate the following integrals. S sin ¹x =dx V1 - x²
Evaluate the following integrals. J dx (tan-¹x)(1+x²)
Evaluate the following integrals. [x cos² (x²) dx
Evaluate the following integrals. TT/2 S™ sin Ꮎ dᎾ
Evaluate the following integrals. 0 TT/6 sin 2 y sin² y + 2 dy (Hint: sin 2 y = 2 sin y cos y.)
Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) = cos x; [TT/2, π]
Simplify the following expressions. .10 d dxJ x² dz 2 z²+1
Evaluate the following integrals. ex - ex ex + ex dx

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