Consider the graph of the functi y = f(x) 14 6 Evaluate the following integrals by...
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...
Use geometry to evaluate the following definite integrals, where the graph of f is given in the figure. LLLLL y=f(x) 1 1 2 3 4 5 6 7 8 x | f(x)dx
(1 point) Book Problem 35 Evaluate the integrals below by interpreting them in terms of areas. 3: (a) 13 |z|dx = % 17:0 - 6) dx = (b) #
ANSWER TO BOTH ASAP (1 point) Consider the graph of the function (): 4 y = g(x) -2 0 4 7. The graph from 1 = 2 to 3 = 6 is a semicircle. Evaluate the following integrals by interpreting them in terms of areas: (a) > *9(e) de = 4 oſ, ºs(z) de = -2pi " ["9(z)de = 445:2pi Note: You can earn partial credit on this problem. (1 point) Find the set on which the curve v= b^...
The graph of Fis shown. Evaluate each Integral by interpreting it in terms of area y = f(x) 0 14 28 425 6 (0) 16°max) dx (0) 17x) dx Need Help? Read It Watch It Talk to a Tutor
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...
ANSWER ASAP Problem 4. (1 point) The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 1. 2. (12) dr = [*(z)dz - /"ra)dz = *** f(x) dx = Note: You can click on the graph to enlarge the image
8.1 The figure shows the areas of regions bounded by the graph of f and the x-axis. Evaluate the following integrals: Area = 15 Area = 20 y = f) Area = 12 d a. (2 Marks) (2 Marks) (2 Marks) Sf(x) dx b. So f(x) dx C. 25"$(x) dx d. 480*f(x) dx e. 35+(x) dx 2 S4F(x) dx (2 Marks) (2 Marks) f. (2 Marks)
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
Exercise 6. The graph of a function f(x) is given. Using the geometry of the graph, evaluate the definite integrals. - 1 2 3 4 51 $*(dx los pcdx S'f(x)dx les srcade (o) f(x)dx 19 P-2f(x)dx