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In Problems 9-13, find or evaluate the integral. r4 9. -dx 9. (5pts.) In(x-1) 10. ]...
1. (a) Find L4 and R4 for the integral
1 (x sin x/2) dx
Show the setup and round the answer to threedecimal places.
(b) Find M4 for the integral
1 (x sin x/2) dx . Show the setup and round the answer to four
decimal places.
Sketch the approximating rectangles on the graph.
(c) Compare the estimates with the actual value
1 (x sin x/2) dx
10.243 . Which estimate is the most accurate?
(d) Express the integral from...
Question 9 Evaluate the integral f(x) dx where 203 f(x) = for x <1 for x > 1 6 7 4 5 3 O2 11 2
2. 10 23 x · [In(x)]2 Jg x+2 In Problems 1-26, evaluate each improper integral, or show why it diverges. po 1 5 1. dx dx 2 3. dx 4. dx 13 1 + x2 5 X 5. dx 6. dx x. In(x) Jo 1 + x2 1 7 dx 8. dx -2 J3 (x - 2)2 1 1 9. dx 10. dx (x - 2) 1 11. dx 12. dx J3 (x+2)3 14 1 1 13. dx 14. dx...
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
Evaluate the following integral. + 6x - 1 dx X-X Find the partial fraction decomposition of the integrand. St*6x=1&x=SO dx Evaluate the indefinite integral. S*** + 6x - 1 3 X-X dx =
Find the following integral, given that S Sadar f(x)dx = 9 and ce)?dx = 13 a lisaslan - /sear -
No 13 and 14
(a) Find an approximation to the integral [** (x2 - 4x) dx using a Riemann sum with night endpoints and n = 8. Rg (b) iffis integrable on [a, b], then Serum f(x) dx lim 10 Fx) Ax, where Ax Als and Ax. Use this to evaluate 4x) dx
(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=
Please answer both questions
Problem #7: Evaluate the following integral. 10 1 x In x dx Problem #7: Save Problem #8: Let f(x, y) = (x + 7y)2 + (y – 10x)2. Find f(0, -6) Problem #8: Save
15
51=dz ProblemS ,,mdx dr Problem, 8 fipam dx § sins(5x)cosa(Sr)dx Problem 6 Problem 4 Problem, 91x-9ds noblen, 7/ǐ Prablem 10 Problem 11 Evaluate each improper integral for, arctan ) dx ill 182+ 9 x2-4 Problem 12 The area of the region bounded by the parabola x-y-3) and the line y x is Problem 13 The base of a solid S is the parabolic region (x,y): xs y perpendicular the y-axis are squares. Find the volume of the solid S...