d f(g(x) dx Referring to the plots of f(x) and g(x) below, calculate: Afrac{d}{dx}f(g(x))\Big|_{x=5} 20 f(x) 15 10 5 15...
1.8 pts D Question 5 Referring to the graph shown, rank the following quantities: f(x)da, L-f(x)dx, &* f(x)dz, Sf(x)dz, and 0 S f()da < Sf(r)dx < L. f(x)dx < Sf(x)dx < 0 f(x)dx < $(x)dx <O<f()dx <S f(x)da of(x)d« <L. f(x)dx <O<S f(x)dx < 8 f(x)dt S f()dx < Sf(x)dx < 0< . f(x)dx < Sf(x)da f(x)d« <S f(x)dx < 0<S f(x)d« < $*f(x)da Question 6
Calculate the definite integral by referring to the figure with the indicated areas, 0 f(x)dx Area A = 1.565 Area B = 2.469 Area C = 5.421 Area D = 1.711 f(x)dx= 0) 6 of 32 (1 complete)
(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=
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
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
Calculate the definite integral by referring to the figure with the indicated areas. 0 b d f(x)dx a B. с Area A= 1.387 Area C= 5.657 Area D = 1.736 Area B = 2.272 0 f(x)dx= с
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]
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
Use the values f(x) dx = 9 and • 5*ox g(x) dx = 6 to evaluate the definite integral. Dar 1920 (a) -8 29(x) dx (b) f(x) dx f(x) dx (0) Stra) – P2 [f(x)-f(x)] dx Need Help? Read it Watch It Talk to a Tutor
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...