2 Consider two functions f and g on [1의 such tat | f(x)dx= 12 J g(x...
8 6. Consider two functions fand gon (2.8] such that Sf(x)dx = 12. Jo(x)dx=5. vex)dx=7, and 59(x)dx = 3. Evaluate the following integrals 2 2 6 a. (58(x)dx=(Simplify your answer.)
The functions f and g are integrable and atunciona tand g ara mag radio and Juste - - -. (vaser 28, and Loved - - 7. Une hes to completo parts (a trous f(x)dx = 8, and g(x)dx = -7. Use these to complete parts (a) through (9) a. f(x)dx = 0 (Simplify your answer.) b. 59(x)dx= [] (Simplify your answer.) c. J 69(x)dx = (Simplify your answer.) d. (1x)dx = 0 (Simplify your answer.) Joix) = f(x)]dx = 0...
18 of 28 (12 complete) 2.37 Consider the functions f(x) = 2x - 6 and g(x) = 5 +3. (a) Find f(g(x)) (b) Find g(f(x)), (c) Determine whether the functions fand g are inverses of each other. (a) What is f(g(x))? f(g(x)) = (Simplify your answer.)
8.2 Suppose that ,* f(x) dx = 6, 8* g(x) dx = 4, and S f(x) dx = 2. Evaluate the following integrals: a. -S2f(x) dx (2 Marks) b. Si(3f(x) – 2g(x)) dx (2 Marks) c. $*f(x)g(x) dx (2 Marks) d. S@dx (2 Marks) [Sub Total 20 Marks]
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
Consider the following functions. f(x)=1/x and g(x)= x^3 Find the formula for (f∘g)(x) and simplify your answer. Then find the domain for (f∘g)(x) . Round your answer to two decimal places, if necessary. Also, Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x) . Round your answer to two decimal places, if ny.
a. 8.2 Suppose that S* f(x) dx = 6, 5+ g(x) dx = 4, and Sf(x) dx = 2. Evaluate the following integrals: - Sa 2f(x) dx (2 Marks) S*(3f(x) - 29(x)) dx (2 Marks) S* f(x)g(x) dx (2 Marks) SIC) dx (2 Marks) C. d. g(x) Sub Total 20 Marksl
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
For f(x) = 8x - 2 and g(x) = x+2 8 find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(5); d. (g of)(5) a. (fog)(x) = (Simplify your answer.) b. (gºf)(x) = (Simplify your answer.) C. (fog)(5) = [] d. (g of)(5) =
4. Given the integrals, [° 8(x) dx =-7, 5*8(x)dx = 6 and 5*g(x) dx = 10, use the properties of integrals to determine the value of the integrals below. a) [°(f(x)+g(x)\dx b) ſ 8(x)dx (4 pts cach) c) $39(x)dx a [ f(x)dx