4. Use the Trapezium Rule with four strips to estimate the area enclosed by the curve y-73, the y-axis, and the lin...
Question 8 a) Find: (3x3 – 5x2 + x - 4) dx (4 marks) b) Use the trapezium rule with 6 strips to approximate the area bounded by the curve y = (x - 1, the x -axis and the lines x = 2 and x = 5 (6 marks)
Use a double integral to find the area enclosed by a loop of the four leaved rose r = 3 cos(2θ). Please mark the answers EXAMPLE 3 Use a double integral to find the area enclosed by a loop of the four leaved rose r-3 cos(26) SOLUTION From the sketch of the curve in the figure, we see that a loop is given by the region So the area is /4 3 cos(28) Video Example dA= n/a 3 cos(26) -π/4...
4. The curve y = rs for 0 < | < 1 is rotated about the z-axis to form a solid of revolution. (a) Find the volume of this solid of revolution 5 marks b) Calculate the surface area of this solid of revolution, leaving your answer in the form of a 5 marks definite integral. (c) Determine in the form of an integral the arc length of this curve from the points at which r0 and r 1, Use...
1(a) . Let A denote the area enclosed by the graph f(x)= 10-x, the x- axis , and the lines x=3 and x =5. Graphing the region and using plane geometry , find A. (b). Let A denote the area enclosed by the graph f(x)= (x-1)^2, the x - axis , and te lines x=2 and x=9. Graphing the region and using plane geometry , we can find that A=. (c). Suppose S4 is the lower sum of the area...
QUESTION 6 Find the area enclosed by the x-axis and the curve x=4+3, y=t-7 O a. 44 + 3t dt 404 + 3t dt 06.261 -2534 -25%A4+31 Oc 125e - eat O d. 12/²3 - eat
4. Find the centroid of the area bounded by the curve x2 (y-4), the x-axis and the y-axis on the first quadrant. A. , 8/5 B. 2, 64/3 C. , 5/4 D. 1/8,5 5. What is the area within the curve r2 16 cos 0? C. 30 A. 26 B. 28 D. 32 6. A uniform chain the weighs 0.50 kg per meter has a leaky 15-liter bucket attached to it. If the bucket is full of liquid when 30...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points 1 - ...) a | and B(x) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: . This part of the assignment is testing that you can find the equation of a line and use this...
2/6 2" (10%) (a) Sketch the graphs of the two functions y=z(4-z) and y=z and mark the finite region (R) enclosed between them. (Identify (R) carefully!) (b) Let W be the volume of the solid of revolution obtained by revolving the above region (R) around the y-axis. (i) Use the shell method to write down the integral for W. (No need to evaluate the integral.) (ii) Repeat part(i) by using the disk method. 2/6 2" (10%) (a) Sketch the graphs...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
whats the area? Sketch the regions enclosed by the given curves. y = VX y = 2x X=25 y y 8 8 6 6 4 15 20 5 10 25 10 15 20 25 у Lenovo c x DE F1 Esc F7 FO FB FS F6 F2 F * ) # 3 $ 4 & 7 2 01 6 9 8 w R T Y U 8 B 6 6 10 15 20 25 5 10 15 20 Find its...