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mathematics
calculus 6th edition

Calculus 6th Edition James Stewart - Solutions

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.x = y2, x = 1; about x = 1
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x, y = √x; about x = 2
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x2, x = y2; about x = –1
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x, y = 0, x = 2, x = 4; about x = 1
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about OC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.ky = cos x, y = 1 – cos x, 0 ≤ x ≤ π
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.y = x2, y = 2/(x2 + 1)
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.y = |x|, y = x2 – 2
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about OC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.y = 1/x, y = x, y = 1/4x, x > 0
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.y = 3x2, y = 8x2, 4x + y = 4, x ≥ 0
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Use calculus to find the area of the triangle with the given vertices.(0,5), (2, –2), (5,1)
Use a graph to estimate the -coordinates of the points of intersection of the given curves. Then use this information and your calculator to estimate the volume of the solid obtained by rotating about the -axis the region enclosed by these curves.y = x3 – x + 1, y = –x4 + 4x 1
Evaluate the integral. 17 - 2x² x² -dx; entry 33
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = ex, y = 2 – x2
Evaluate the integral. (5 X Jo x + 10 - dx
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the -axis the region bounded by these curves.y = 3 sin(x2), y = ex/2 + e–2x
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = x cos x, y = x10
Evaluate the integral. 3x √3 - 2x -dx; entry 55
Evaluate the integral.∫sin3x cos2x dx
Evaluate the integral. 3 sin ³x COS X dx
Evaluate the integral using integration by parts with the indicated choices of u and dv.∫θ cos θ dθ; u = θ, dv = cos θ dθ
Evaluate the integral. (5 Jo ,-0.6y ye dy
Evaluate the integral. se sec³(x) dx; entry 71
Evaluate the integral. sin x + sec x tan x - dx
Evaluate the integral. 3/4 sin³x cos³x dx TT/2
Evaluate the integral.∫x cos 5x dx
Evaluate the integral. #/2 cos ( So 1 + sin e de 0
Evaluate f² (√/1 − x² − √/1 − x³) dx. -
Evaluate the integral. (2√3 1²√³√16 - x² X-3 0 dx
Evaluate the integral. e20 sin 30 d0; entry 98
Evaluate the integral.∫xe–x dx
Evaluate the integral. TT/2 cos³x dx
Evaluate the integral. St dt (2t + 1)³
Evaluate the integral.∫tan3θ dθ
Evaluate the integral. 2 1/2 1 1³√1²-1 - dt
Evaluate the integral. 2t So (7-3)²" (t dt
Evaluate the integral.∫rer/2 dr
Evaluate the integral. *#7/2 Jo sin³ 0 cos²0 de
Evaluate the integral. IC .2 √√√x² - 1 dx x
Evaluate the integral.∫sin2 (πx) cos5 (πx) dx
Evaluate the integral. X 3-x4 dx
Evaluate the integral.∫t sin 2t dt
Evaluate the integral. 1 y²-4y - 12 dy
Evaluate the integral. sin³ (√x) dx X)
Evaluate the integral. √x = 69 - dx
Evaluate the integral. 1 x²√25-x² - x² dx
Evaluate the integral. arctan y 5²₁ dy −11+ y²
Evaluate the integral.∫x2 sin π x dx
Evaluate the integral. 1 12x - dx
Evaluate the integral. *8 * √x dx
Evaluate the integral. L°₂ (u² − u² + u²) du
Evaluate the integral. $2²3, dr dt
Evaluate the integral. -2 (3u + 1)² du
Evaluate the integral. *2π 4 cos e de
Evaluate the integral. (2v + 5)(3v1) dv
Evaluate the integral. ² x(2 + x³) dx
Prove that fx dx = b² − a² 2
Evaluate the integral. √t (1 + t) dt
Evaluate the integral. f² (3 + x√x) dx Jo
Prove that b³ - a³ f₁ x² dx = 5² 3 D
Evaluate the integral. S√Zt dt 21 10
Evaluate the integral. p T-X6J
Evaluate the integral. 2 [² ( 49² + ²/3) a dy ,3
Evaluate the integral. f(y − 1)(2y + 1) dy Jo
Evaluate the integral. ² y + 5y² ,3 J1 dy
Evaluate the integral. 1/4 sec²t dt
Evaluate the integral. fx (√x + √x) dx
Evaluate the integral. *π/4 Jo sec 0 tan 0 de
Evaluate the integral. S³ (2e² + 4 cos x) dx
Evaluate the integral. f² (1 + 2y)² dy J1
Evaluate the integral. 5 X dx
Evaluate the integral. cosh t dt
Evaluate the integral. 3x - 2 1.³ ³. X -dx
Evaluate the integral. Jo (4 sin 0 - 3 cos 0) de
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = x2 + 12/x – 2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is relevant
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.xy = x2 + 4Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is relevant to every
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = ex – xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is relevant to every
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = 2x3 + x2 + 1/x2 + 1Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is
Find f.f'(x) = cos x – (1 – x2)–1/2
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = (x + 1)3/(x – 1)2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is
Find f.f'(x) = 2ex + sec x tan x
Find f.f'(x) = √x3 + 3√x2
Find f.f'(x)= sinh x + 2 cosh x, f(0) = 2
Find f.f'(u) = u2 + √u/u, f(1) = 3
Find f.f"(x) = 1 − 6x + 48x2, f(0) = 1, f'(0) = 2
Find f.f"(x) = 2x3 + 3x2 – 4x + 5, f(0) = 2, f(1) = 0
Find the minimum value of the area of the region under the curve y = x + 1/x from x = a to x = a + 1.5, for all a > 0.
If f is a differentiable function such that f(x) is never 0 andfor all x, find f. f(t)dt = [f(x)]²
(a) Find the Riemann sum for f(x) = sin x, 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Give your answer correct to six decimal places.) Explain what the Riemann sum represents with the aid of a sketch. (b) Repeat part (a) with midpoints as sample points.
If where find f'(π/2). f(x) g(x) Jo 0 1 √1 + 1³ =dt

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