2.99 See Answer

Question: Evaluate the integral. f10 (4√u + 1


Evaluate the integral.
f10 (4√u + 1)2 du


> The base of a solid is the region bounded by the parabolas y = x2 and y = 2 – x2. Find the volume of the solid if the cross-sections perpendicular to the -axis are squares with one side lying along the base.

> Find the area of the region bounded by the given curves. y = 1/x, y = x², y= 0, x= e

> The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

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> Evaluate the integral. f-12 (x – 2|x|) dx

> Evaluate the integral. f21 (8x3 + 3x2) dx

> Evaluate: (a). f10d/dx (earctan x) dx (b). d/dx f10 earctan x dx (c). d/dx fx0 earctan t dx

> (a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the inflection points. (e). Use the information from parts

> Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = cos?x, |x|< n/2, y = about x = T/ T/2

> (a). Write f20e3x dx as a limit of Riemann sums, taking the sample points to be right endpoints. Use a computer algebra system to evaluate the sum and to compute the limit. (b). Use the Evaluation Theorem to check your answer to part (a).

> If f60f (x) dx = 10 and f40f (x) dx = 4, find f64f (x) dx.

> Express as a definite integral on the interval [0, &Iuml;&#128;] and then evaluate the integral. lim 2 sin x; Ax

> Evaluate the integral. f 10/ (x – 1) (x2 + 9), dx

> Find the derivative of the function. F (x) = fx0t2/1 + t2, dt

> Graph the function f (x) = cos2x sin3x and use the graph to guess the value of the integral f2π0f (x) dx. Then evaluate the integral to confirm your guess.

> The Fresnel function was defined in Example 4 and graphed in Figures 6 and 7. Figures 6: Figures 7: (a). At what values of does this function have local maxi mum values? (b). On what intervals is the function concave upward? (c). Use a graph to solv

> Let g (x) = f 9x2), where f is twice differentiable for all x, f'(x) > 0 for all x ≠ 0, and f is concave downward on (-∞, 0) and concave upward on (0, ∞). (a). At what numbers does g have an extreme value? (b). Discuss the concavity of g.

> Use a graph to give a rough estimate of the area of the region that lies under the curve y = x√x, 0 < x < 4. Then find the exact area.

> Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). dx Vx? + 1

> Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). cos x V1 + sin x Sin X

> Evaluate the integral. f10 ex/1 + e2x, dx

> Evaluate the integral. f sec θ tan θ/1 + sec θ, dθ

> Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = Vĩ, y = x; about y = 2

> Evaluate the integral. f tan-1 x dx

> Evaluate the integral. f e3√x dx

> (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 par

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> Evaluate the integral. f12 (x – 1)3/x2 dx

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> Evaluate the integral. f41 x3/2 lnx dx

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> Evaluate the integral. fπ/4-π/4 t4 tan t/2 + cos t, dt

> Evaluate the integral. f50 ye-0.6y dy

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> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x² – y? = a², x = a + h (where a > 0, h> 0); about the y-axis

> Evaluate the integral. f21 ½ - 3x, dx

> A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450m above the ground. (a). Find the distance of the stone above ground level at time t. (b). How long does it take the stone to reach the ground? (c). With what velocit

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> (a). Evaluate the Riemann sum for f (x) = x2 &acirc;&#128;&#147; x, 0 (b). Use the definition of a definite integral (with right end - points) to calculate the value of the integral (c). Use the Evaluation Theorem to check your answer to part (b). (d).

> Evaluate the integral. f10 eπt dt

> Evaluate the integral. f10 sin (3πt) dt

> Evaluate the integral. f10v2 cos (v3) dv

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> Evaluate the integral. f10 x/x2 + 1, dx

> Evaluate the integral. f (1 – x/x)2 dx

> Evaluate the integral. f10 (1 – x)9 dx

> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x' + 1, y= 9 – x²; about y = -1

> Evaluate the integral. f0π/3 sin θ + sin θ tan2 θ /sec2θ, dθ

> (a). If g (x) = 1/(√x -1), use your calculator or computer to make a table of approximate values of f12g (x) dx for t = 5, 10, 100, 1000, and 10,000. Does it appear that f∞2g (x) dx is convergent or divergent? (b). Use the Comparison Theorem with f (x) =

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> Evaluate the integral. fr0 (x4 – 8x + 7) dx

> Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be (a) left endpoints and (b) midpoints. In each case draw a diagram and explain what the Riemann sum represents. y= f(x) 6 2. 2.

> (a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the inflection points. (e). Use the information from parts

> (a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the inflection points. (e). Use the information from parts

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> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. If f'(c) = 0, then f has a local maximum or minimum at c. 2. If f has an absolute minimum value

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> Find the area of the region bounded by the given curves. y = x², y= 4x – x²

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> (a). Write the definition of the definite integral of a continuous function from a to b. (b). What is the geometric interpretation of fba f (x) dx if f (x) > 0? (c). What is the geometric interpretation of fba f (x) dx if f (x) takes on both positive and

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> A company modeled the demand curve for its product (in dollars) by the equation Use a graph to estimate the sales level when the selling price is $16. Then find (approximately) the consumer surplus for this sales level. 800,000e/S000 p = x + 20,00

2.99

See Answer