QUESTION 6 Find the area enclosed by the x-axis and the curve x=4+3, y=t-7 O a....
t2-2t, y =vt and the y-axis. Find the area enclosed by the curve x t2-2t, y =vt and the y-axis. Find the area enclosed by the curve x
(3) Find the area bounded by the curve x(t) = 3t-t2, y(t) = 3.li and the y-axis. 3 N 1 2
3. Find the total area of the region enclosed by the curve y=xsin x and the x-axis from (0,37). The graph is shown below. Show all of your work! (Hint: You will need multiple integrals here)! (8 pts)
12 10. Find the area enclosed by the polar curve 2 11 cos (80). 11T Hide Elapsed: 0000 27 Instructions O22π 11. This question is worth 20 points. You must complete both parts. Parts (a) and (b) are not related and should be answered as separate, distinct problems. θ2,0 θ (a) (10 points) Graph the polar curve r (b) (10 points) Find the surface area given by rotating the curve ya froma1 to 3 about the z axis. 12. This...
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
Consider the curve X = 42 y=ť, 0 <t<1 Setup the integral for the area of the surface obtained by rotating the curve about 27 (2+4 + 3t") dt [ 26 (28 + 3t) dt 2*t* 4 +01+ dt 27tº /2 + 3* dt [ 2013 (4+9t? dt
1-Cos(24) as O t 7, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(r, y) ()) m, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(x,)-().) (6) Consider the curve expressed by the polar equation T-0, as 0 1-Cos(24) as O t 7, which I have drawn for you below. Find the...
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...
4. Use the Trapezium Rule with four strips to estimate the area enclosed by the curve y-73, the y-axis, and the lines y-| and y-8, (i) the curve p-2/9, the p-axis, and the lines p = 2 and p 24, and w=쫄. (ii) the curve z = cos w, the w-axis, and the lines w 4. Use the Trapezium Rule with four strips to estimate the area enclosed by the curve y-73, the y-axis, and the lines y-| and y-8,...
Find the exact area of the surface obtained by rotating the curve about the x-axis. y=1+5x, 1sx57 a. 309/10 b. 3097/5 c. 3097/15 d. 3337/5 e. 333 1/25 a C b oc