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Integrals

Limits, L'Hopital's Rule and Integrals

1. Evaluate 2) 2. Differentiate the function f(x) = ln(2x+3) 3. Find lim x∞ (e2x / (x + 5)3). Apply L'Hopital's rule as many time as necessary, verify your results after each application. 4. Evaluate ∫xsinh(x)dx See attached file for full problem description.

Integration

1.R is the region that lies between the curve y = (1 /( x2 + 4x + 5) ) and the x-axis from x = -3 to x = -1. Find: (a) the area of R, (b) the volume of the solid generated by revolving R around the y-axis. (c) the volume of the solid generated by revolving R round the x-axis. 2.Evaluate: ∫ sinh6 x cosh xdx.

Calculating Definite Integrals

Calculate, correct to the nearest hundredth, 1.5 ∫ (2.73x^2 - 8.41x + 7) dx = 0.5 1.55 1.69 2.27 2.88 3.81 7.01 9.44 12.54 26.71 none of these

Integration : Area of a Bounded Region

The average value of f(x) = 1/x on the interval [4, 16] is (ln 2)/3 (ln 2)/6 (ln 2)/12 3/2 0 1 none of these Find the area, in square units, of the region bounded by the the x axis and the function y = 16 - x^2. 32/3 3

Finding Integrals

17. Find the antiderivative of (x^2)(1 + x^3)^5 . (1 + x^2) (1 + 9x^3)^5 + C (1/18)(1 + x^3)^6 + C (1/18)x(1 + x^3)^6 + C (1/18)x2(1 + x^3)^6 + C none of these 19. ∫ (6e^3/x)x^-2 dx = 2e^-3/x + C -2e^3/x + C (-1/2)e^3/x + C

Integral and profit function

Please choose the correct answer: Q#16) suppose that the price-demand equation is given by p = 9 - ln x, where 0 < x <= 200, x is in thousands, and the cost of manufacturing is $3 per item. What price will maximize profit? $2.00 $2.60 $3.00 $3.20 $4.00 $4.50

Integral and derivative

Please choose the correct answer: Q#20) True or False: if f(x) = ln(9 + x) then f '(x) = 1/(9 + x) True False Q#18. b b c c Given that &#8747; x^2 dx = 5, &#8747; x^5 dx = 3, &#8747; x^2

Average value and tangent line

Please choose the correct answer: Q#11) The average value of f(x) = 1/x on the interval [2, 8] is (ln 2)/3 6/5 (ln 6)/6 (ln 4)/2 0 1 none of these Q#1. Find the equation of the tangent line to y = ln x at the point where x = 2.

Integrate

Please choose the correct answer: Q#14) Calculate, correct to the nearest hundredth, 3.75 &#8747;(2.73x^2 - 8.41x + 7) dx = 0.5 1.55 1.69 2.27 2.88 3.81 7.01 9.44 12.54 26.71 none of these Q#15) 3 &#87

Objective Question

Choose the correct answer (Please show the process) 7. &#8747;2/x^2/3 dx = (2/3)x^1/3 + C 6x^1/3 + C (2/3)x^2/3 + C 6x^2/3 + C none of these 8. &#8747;e^x(3e^x + 1)^-2/3 dx = 3(3e^x + 1)^1/3 + C (3/5)(3e^x + 1)^5/3 + C (1/4)(3e^

Estimating a Definite Integral

The values of the function A'(t) are given by the following table: See attached file for full problem description. Approximate the area under the graph of A'(t) from t = 0 to t = 5 using left and right sums over five equal subintervals. Use these sums to estimate the value of the definite integral of A'(t) from 0 to 5.

Definite Integral

Using the information about integrals of x^2 and x (between 1 and 6 and between 6 and 10), what is the value of the definite integral of (x^2 - 6x) between 1 and 10? See the attached file for more information.

Definite Integral

Using the graph and the information given, what is the value of the definite integral of f(x) between b and 0? See the attached Word file for the picture of the graph of f(x).

Finding Integrals

Q#1) Find 6/5 &#8747; ( x^ - 5 ---- ) dlx (Check by differentiating) X^3 Q#2) x^6 e^x - 4x &#8747; -------------------- dlx X^6 Q#3) Find all antiderivatives if dl A ------ =

Rates of Growth and Integration

Q#1) dA --- = -6t^9 - 6t^4 + 4 dt A= ? Q#2) The rate of growth of the population, N(t), of a newly incorporated city t years after incorporation is estimated to be dN --- 1200sqrt(t) + 400, 0 < t < 16 (less than or equal to) dt If the population was

Evaluate the Integrals

Please explain the steps and solutions, thanks: Evaluate the integrals: (ln x)² a) &#8747; &#8254;&#8254;&#8254;x&#8254;&#8254;&#8254; dx b) &#8747; x²e^x³dx c) x³ &#8747; &#8254;&#8254;&#8254;&#8254;&#8254; dx 1 + x² keywords: in

Stokes Theorem

Stokes Theorem. See attached file for full problem description. Use Stokes Theorem to evaluate....

Evaluating Definite Integrals

pi Use the fact that &#8747; u²du = pi³/3 to evaluate the definite integral. º pi a) &#8747; (pi x + x²)dx º ²x b) show that 2pi &#8804; &#8747; &#8730;1 + 3

Integration

Integration of Exponential Functions. See attached file for full problem description.

Integrals : Volume of a Hollow Cylinder

A 6.00 in radius cylindrical rod is 2 ft long. Use a differential to approximate how much nickel (in in^3) is needed to coat the entire rod with the thickness of .12 in. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Double Integral

Evaluate the double integral integral from y=0 to y=3 of integral from x=0 tp 1-y of (x+y)dxdy int ( int (x+y), x=0..1-y), y=0..3)