8.1 The figure shows the areas of regions bounded by the graph of f and the...
In the figure, the regions A, B, C and D bounded by the x-axis and the graph off have the following properties: • Region A and Region D each have area 300. • Region B and Region C each have area 192. B Use the figure to calculate the following definite integral. Sice) dx = 0
EXAMPLE 4 Evaluate the following integrals by interpreting each in terms of areas. (a) y=V25-2 lov ✓ 25 - 2 dx or 10 + y = 25 (x - 3) dx SOLUTION (a) Since Rx) = V25 - x2 > 0, we can interpret this integral the area under the curve y = 25 - X2 from 0 to But we get x2 + y2 = 25, which shows that the graph of ris a quarter-circle with radius in the...
In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following properties: Region A and Region D each have area 100 • Region B and Region Ceach have area 64. 019 Use the figure to calculate the following definite integral 2018
Consider the graph of the functi y = f(x) 14 6 Evaluate the following integrals by interpreting them in terms of areas: [* f(e)dx = 4 a» [° s(m) do = 6 <-> ["s(e) dx = 8 (0 [° f(x) dx = 12 = 12
Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above. a) Find the area of R. b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. c)...
f(x)dx=_, | f(r)dr? Given that what IS Preview answer Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1-5, A2-4, A3-2 and A4:1 y-fx) A1 АЗ A2 igure is NOT to scale Enter your answer as a whole number Evaluate dx. 1 + e1.82z 71.7 answer If -16 f(x)dx = 12 and r-16 g(x)dx = 15 J- 85 and -16 h(z)dz 21 -85 what does the following integral...
3. Refer to the graph as shown in Figure A3. (a) Determine the first moment of area of the shaded region formed by arc y=x? about y-axis, as shown in Figure A3. (5 marks) (b) Calculate the area of the shaded region, as shown in Figure A3. (3 marks) 40 35 30 25 y = x2 (V) 20 15 10 5 0 2 (x) Figure A3
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (Ix): (4 marks) (b) the second moment of area about y axis (Iy); (4 marks) c) the second moment of area of about z (Iz), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x X 4 Figure A4 5. 1 Given the differential equation: dy +-y 3x2 dx х Find (a) the general...
Let
f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and
2-2sin(sqrtx) for [0, (x^3)/4]. the graph of f is shown in the
figure above. Let R be the regiok bounded by the graph of f and the
x-axis.
for -25=co for osca Let I be the function defined by 1 (2) - {}(2+2) (2-2n The graph of fis shown in the figure above. Let R be the region bounded by the graph off and the ads (a) Find the...
a) determine the area bounded by the graph of
f(x)=3x2 and the x axis between x=0 and x=1
b) evaluate intergral
2.0 – 2 -do C2 - 2.0