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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Find the limit. lim arctan t, e2 1-0 →→00 In t t
Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.)kr(t) = 〈√t, t, t2), 1 < t < 4
Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.)r(t) = 〈t, ln t, t ln t〉, 1 < t < 2
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases.r(t) = 〈t3, t2〉
Find the derivative of the vector function.r(t) = 〈t sin t, t2, t cos 2t〉
Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.)r(t) = 〈sin t, cos t, tan t〉, 0 < t < π/4
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which increases.r(t) = 〈t, cos 2t, sin 2t〉
Find the velocity, acceleration, and speed of a particle with the given position function.kr(t) = 〈t2 +1, t3, t2 - 1〉
Find the derivative of the vector function.r(t) = 〈tan t, sec t, 1/t2〉
Evaluate the integral. 1 √4y² - 4y - 3 S- - dy
Prove Property 6 of integrals.Data from Property of integral 6 ·b If f(x) > 0 for a ≤ x ≤ b, then f(x) dx > 0.
Evaluate the integral. x² - 2x - 1 (x - 1)²(x² + 1) -dx
Evaluate the integral. √√√x+1 3 √√x - 1 xp. dx
Evaluate the integral. Ji (In x)² 3 x³ dx
Evaluate the integral. x² + 1 (x² - 2x + 2)² dx
Evaluate the integral.∫tan3(2x) sec5(2x) dx
Evaluate the integral. x + 4 x² + 2x + 5 -dx
Evaluate the integral. -1 x³ sec x dx
Evaluate the integral. 5 3w1 Jo w + 2 dw
Evaluate the integral.∫cos x ln(sin x) dx
Evaluate the integral. fx√1 – x4 dx -
Evaluate the integral. 3x² + x + 4 x² + 3x² + 2 dx
Evaluate the integral. dx e*√1-e-2x
Evaluate the integral. r 3 S= Jo √4 +r² dr
Evaluate the integral. 1³²2₂ | x² - 4x|dx
Evaluate the integral. TT/3 Jo tan³x secºx dx
Evaluate the integral. TT/2 cos t 1/² √√₁ + sin²r dt
Evaluate the integral. 1 x3 - - dx 1
Evaluate the integral. xp z(x )+ x 1
Evaluate the integral. In ex in 10 e²√e* - 1 et + 8 - dx
Evaluate the integral. 1 + x V1-x dx
Evaluate the integral.∫tan5x dx
Evaluate the integral. x² + 4x + 13 dx
Evaluate the integral. e² sin(t - s) ds
Find the volume of the solid obtained when the region under the curve y = x√4 – x2, 0 ≤ x ≤ 2, is rotated about the y-axis.
Evaluate the integral. *#/4 x sin x - dx 3 cos³x
Evaluate the integral. 2x - 1 2x + 3 dx
Evaluate the integral.∫tan6(ay) dy
Evaluate the integral. S x³ + 2x x² + 4x² + 3 dx
The region under the curve y = tan2x from 0 to π/4 is rotated about the x-axis. Find the volume of the resulting solid.
Evaluate the integral. dx z/ɛ( z* - +) zx
Evaluate the integral. √√3 - 2x - x² dx
Evaluate the integral. tan³0 cos¹0 de
Evaluate the integral. x³ x³ + 1 .3 dx
Evaluate the integral. "w/2 1 + 4cotr J/4 4 cotx - dx
First make a substitution and then use integration by parts to evaluate the integral.∫t3e–t2 dt
Evaluate the integral. dx x(x² + 4)²
Evaluate the integral. 1 x + x3/2 -dx
Evaluate the integral. x³ sin x dx X
Evaluate the integral. x² + 3x² + 1 r5 +5x3+5x dx
Evaluate the integral. 1 - tan 0 - de 1 + tan 0
Evaluate the integral. sin o 3 cos³ do
Evaluate the integral. x²-3x + 7 (x² - 4x + 6)² dx
Evaluate the integral.∫sin 4x cos 3x dx
Evaluate the integral. S¹* cos²0 tan²0 de Jo
Evaluate the integral. TT/2 π/6 cot²x dx
Evaluate the integral. x³ + 2x² + 3x - 2 (x² + 2x + 2)² -dx
Evaluate the integral. (x + 2)³ dx
Evaluate the integral. [/4 tan³0 sec ³0 de Jo
Evaluate the integral. *π/2 Jπ/4 cot³x dx
Evaluate the integral. 2.x (1/2) xe fo² (1² + 2x)² Jo dx
Evaluate the integral. S sec 0 tan 0 sec²0- sec 0 do
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the function and its antiderivative (take C = 0).k∫(2x + 3)exdx
Evaluate the integral. #/3 √tan 0 T/4 sin 20 - do
Evaluate the integral.∫cot3α csc3 α dα
Evaluate the integral.∫csc 4x cot6x dx
Evaluate the integral.∫θ tan2θ dθ
Evaluate the integral. tan ¹x 2 x² dx
Evaluate the integral.∫csc x dx
Evaluate the integral. (π/3 π/6 csc ³x dx
Evaluate the integral. Se²√1 + e² dx
Evaluate the integral. S /1 + e* dx
Evaluate the integral.∫cos πx cos 4πx dx
Evaluate the integral. 1 + sin x 1 – sin x TH - dx
Evaluate the integral.∫x5e–x3 dx
Evaluate the integral. cos x + sin x sin 2.x dx
Evaluate the integral.∫ sin 5θ sin θ dθ
Evaluate the integral. 1 - tan²x sec²x dx
Evaluate the integral. X x² = a* 4 X - dx
Show that 1/3Tn + 2/3Mn = S2n.
Evaluate the integral. dx cos x - 1
Evaluate the integral. S 1 x√4x + 1 dx
Evaluate the integral. 1 ²√4x + 1 dx
Evaluate the integral.∫t sec2(t2) tan4 (t2) dt
Evaluate the integral. 1 x√4x² + 1 S- dx
Evaluate the integral. dx x(x + 1)
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the integrand and its antiderivative (taking C = 0).∫sin3x cos4x dx
Find the area of the region bounded by the given curves.y = xe–0.4.x y = 0, x = 5
Find the area of the region bounded by the given curves.y = 5 ln x, y = x ln x
Evaluate the integral. dx x + x√x
Evaluate the integral. dx √x + x√√x
Evaluate the integral.∫ (x + sin x)2 dx
Evaluate the integral. fx √x + c dx
Evaluate the integral. x ln x x² - 1 dx
Evaluate the integral. √ dx x²√√4x² - 1
Evaluate the integral. √ √x e√³ dx
Evaluate the integral.∫cos x cos3 (sin x) dx
Evaluate the integral. 1 x + √√x dx xp.
Evaluate the integral. sin 2x 1 + cos x dx
Evaluate the integral. In(tan x) #/3 J/4 sin x cos x - dx

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