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    Integrals

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    Double Integration : Joint PDF, Marginal and Conditional Densities

    Please see the attached file for the fully formatted problems. Suppose that X and Y are continuous random variables with the joint probability density function k(x+y) for 0<x<1,0<y<2 f(x,y) = 0 otherwise (a) Find k, E(X), E(Y), V(X), V(Y), and Cov(X, Y). (b) Are X and Y independent ? (c)

    Limits, L'Hopital's Rule and Integrals

    1. Evaluate 2) 2. Differentiate the function f(x) = ln(2x+3) 3. Find lim x&#61664;&#8734; (e2x / (x + 5)3). Apply L'Hopital's rule as many time as necessary, verify your results after each application. 4. Evaluate &#8747;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: &#8747; sinh6 x cosh xdx.

    Calculating Definite Integrals

    Calculate, correct to the nearest hundredth, 1.5 &#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

    Evaluating Definite Integrals

    Calculate, correct to the nearest hundredth, 1.5 &#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 A jewelry floor safe with a square base is to be made

    Integration : Area of a Bounded Region

    Please help with the following problem. Provide step by step calculations for each. 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 b

    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. intregral (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

    Derivative and integral

    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 ∫ x^2 dx = 5, ∫ x^5 dx = 3, ∫ x^2 dx = 7/2, and

    Tangent Line and Average Value

    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.

    Price-demand and integrals

    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

    Examples of Definite Integrals

    Please choose the correct answer: Q#14) Calculate, correct to the nearest hundredth, 3.75 ∫(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 ∫ (x -

    Examples of Choosing the Correct Integration

    Choose the correct answer (Please show the process) 7. ∫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. ∫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^x + 1)^4

    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 Values

    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.

    Value of the 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).

    Find the Integrals

    Q#1) Find 6/5 ∫( x^ - 5 ---- ) dlx (Check by differentiating) X^3 Q#2) x^6 e^x - 4x ∫ -------------------- dlx X^6 Q#3) Find all antiderivatives if dl A ------ = -7t^8 - 2t^2 +2

    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 5

    Evaluating the Given Integrals

    Please explain the steps and solutions: Evaluate the integrals: (ln x)² a) ∫ ‾‾‾x‾‾‾ dx b) ∫ x²e^x³dx c) x³ ∫ ‾‾‾‾‾ dx 1 + x².

    Stokes Theorem

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

    Mathematics: 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

    Evaluating Integrals

    Evaluate the definite integral using a graph of the integrand over the interval integration. 0 &#8747; &#8730;9 - w²dw -3

    Area Under the Curve of a Piecewise Function

    Please evaluate the integrals assuming that f is the function show on the graph on the attached document. Please explain the steps and solutions. See attached file for full problem description.