MATH 182A Lecture 2: 6.1_areas-between-curves

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goldduck946

28 Sep 2016

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Finding the area between curves is very similar to nding the area underneath a curve. The area between f and g is simply the di erence between the area under f and the area under g. Find the area between the curves: y = 5x x2 y = x. We need to nd the points of intersection between the curves: x = 5x x2 x2. 4 = 0 x(x 4) = 0 x = 0 x = 4. Now we can use those as the limits of integration: A = z b a (cid:20)f (x) g(x)(cid:21)dx. Find the area between the curves: y = x y = x2 y f g x. We need to nd the points of intersection between the curves: x = x2 x2. X = 0 x(x 1) = 0 x = 0 x = 1. Now we can use these as the limits of integration: A = z 1 x x2dx x3 (cid:20) x2.

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Show transcribed image text /www.mathel com/Student/Playerflomework.aspxZhome MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 4.3.5 Find the area under the given curve over the indicated interval yFX2; [2,4] The area under the curve is ( Simplify your answer.)
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ve Do Homework-Charles Kimber- Internet Explorer https//www TII MATH1 160ãMinear Aug18-Sat m Homework: Practice HW9 13 Score: 0 of 1 pt 10 of 4.4.3 Find the area under the graph of f over the interval [-2,3]. s.c Un 2x x>1 The area is. (Simplify your answer.) 5 we ng hel tor etw c.u en te Enter your answer in the answer box and then click Check Answer n/2 rma o find the area above a certain value ted to find area under curve calculator

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1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

MATH 182A Lecture 2: 6.1_areas-between-curves

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