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    Integrals

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    Basic Mathematics Problems Involving Digits and Word Problems

    Find the greatest common factor for the following group of numbers: 24, 36, 48 A rectangular picture window is 5ft by 8ft. Polly wants to put a trim molding around the window. How many feet of molding should she buy? (Can you draw a picture?) Write the following in standard form of a number (Hint: use a number char

    Integrals, Vector Fields, and Differential Equations

    Please see attached 1) To find the general integral of the differential equation, discuss existence et uniqueness and find the particular integral that passes for the point (1;5/2) 2) Considering the linear equation of the 2nd order z'' - (2/x) z' + (2/ x2)z = 10 / x2 , x > 0 .

    Learning to Sketch Areas under the Standard Normal Curve

    Sketch the areas under the the standard normal curve over the indicated intervals, and find the specified areas. 14. To the left of Z = 0.72 18. To the right of Z = -2.17 24. Between Z = -1.40 and Z = 2.03 34. P (z ≤ 3.20) 42. P (-1.78 ≤ z ≤ -1.23) 46. P (-2.37 ≤ z ≤ 0)

    Sequences and Area

    See the attached document for proper formatting. Find the centroid of the region bounded by the curves y = x + 2, y = x^2. Set up the integral (do not integrate) of the area of between of the curves: r = sin(2theta) and r = sin theta (Hint. Sketch the curves, identify the region and use symmetry.) Give an example

    Integration and Fundamental Theorem Calculus

    Question 1 Find ∫ x3+4 ________________________________________x2 dx Question 2 Apply the Fundamental Theorem of Calculus to find the derivative of: h(x)= x∫2^/¯u-1dx Question 3 Evaluate: ∫2cos2 xdx

    Antiderrivatives (Integrals)

    Please show any work Find the anti-derivative. 2. f(x) = 5x 4. g(t) = t^2 + t 6. g(t) = t^7 + t^3 8. g(x) = 6x^3 + 4 10. f(x) 5x - (sq rt of x) 12. r(t) = 1/t^2 14. p(t) = t^3 - t^2/2 - t 16. f(t) = 2t^2 + 3t^3 + 4t^4 Fin the indefinite integrals in the following. (all have the symbol for indefini

    Lagrange

    Please see attachment Compute the Lagrange interpolating polynomial L(x) for the function f(x) f (x) = √(cos(ax)) a = 1.1125 passing through the points (0, f(0)), (0.5, f(0.5)) and (1, f(1)). Let S1 be the first Simpson' rule approximation to Show that

    Newton's Interpolating

    See attachment. Use Newton's interpolating polynomial to approximate the function: f (x) = e^ (-ax2) a = 1.1125 Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x). ii) Compute the value of the integral accurate to 1 decimal place. iii) Compute sufficient trapez

    Integration and other topics

    See attachment for fomatting 1 Evaluate 3∫1 1-∫-2 (x2y-2xy3)dydx 2 Correctly reverse the order of integration, then evaluate 1∫0 1∫y xeydxdy 3 The plane region R is bounded by the graphs of y=x and y=x2 . Find the volume over R and beneath the graph of f(x, y) = x + y. 4 Find t

    Curve of Regression (Part of a Physics Experiment)

    I have a defined curve with an associated 2nd order polynomial equation. I want to understand how to calculate the area under the curve as I have it denoted on the attached pdf file. Also is the integration relative to the x,y limits I have shown.....or is it truly the total area under the curve relative to the x-axis? Sho

    Area bounded by two curves.

    (Please see the attachment for fig.) Let R and S be the regions in the first quadrant shown in the figure. The region R is bounded by the x-axis and the graphs of y = 2 - x^3 and y = tan x. The region S is bounded by the y-axis and the graphs of y = 2 - x^3 and y = tan x. a) Find the area of R. b) Find the area of S

    Integration of Functions

    Integrate for upper limit 3 and lower limit -3 1) ( 20 / (1 + x^2) - 2 ) dx The 2 is a separate term 2) ( 20^2/ (1 + x^2)) ^2 - 4 ) dx Note. Both numerator and denominator are squared The 4 is a separate term 3) ( 20/ (1+x^2) - 2 )^2 dx The 2 is a separate term 4) Integrate

    The area of the region bounded by two curves

    Please see the attached file. Part a. Graph the region bounded by y = 12 - x^2 and y = -x Part b: Give a formula in terms of x-integral(s) for the area of this region. Do not compute the area. Part c: Give a formula in terms of y-integral(s) for the area of this region. Do not compute the area.

    Definite Integral and Area

    Two questions on definite integral and area. See the attached file. 3. Read the statement of this problem very carefully. The graph of g(x) is given below on the interval [-3,5]. Regions A, B and C are labeled in the graph. The area of region A is 32/3, the area of region B is 32/3, and the area of region C is 32/3. Co

    Examples of Integration

    Suppose that f and g are continuous functions and (integral sign) from 2 - 0 of f(x) dx = 5 and (integral sign) from 2-0 of g(x) dx = 13. Compute the following. If the computation can not be made because something is missing, clearly explain what is missing. a). (integral sign) from 6 - 4 of f(x-4) dx answer key says: (int