All work please
Evaluate: SỐ 9(x) dx, where g(x) = x2 for x 5 2 = 5 + x for x > 2 Find the average value of y = 4x3 + 2x over the interval [–2, 1]
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
10. (16) Find each indefinite integral using u-substitution: a. x?(1–2x")*dx b. ſxcos(x2 – 1) dx
2. For the function f(x)= (2x² – 3, x>2 19-2x, x<2 find the limits or explain why they do not exist. (a) lim f(x) 1-2+ (b) lim f(x) (e) lim f(x) X2
Evaluate the integral. S (2x-1) In(18) dx (x2 – x)In 18x - +x+C 2 + x + C (21-x]ın 18x** 0 (x2 - x)In 18- x2 +x+C 0 (x2-x)in 18x - 2 + 2x +C
Determine the following integrals T Sin(x) 1 + x² dx 2). xe 2x dx Idy dx + P(x) y = Q(x) integration factor Solve dy Ex dx sinx the following differenti al equations ... + 3y t? dy F) (l+x) dx +y=vx V: eSP(x) dicas
10. (16) Find each indefinite integral using u-substitution: a. (x*(1-2x°)* dx b. fxcos (x2 - 1) dx
f [10 pts] Given f(x) = 2x+3 – 1. a. Find the Domain and Asymptote b. Sketch the graph of f(x)
2x 3) Let f(x) = 3V9+x2 a) Evaluate the definite integral 1393 f(x)dx, using Trigonometric substitution. b) Find f(x)dx, using Trigonometric substitution. c) Is there any other way to compute the integral of part b). Explain. If yes, then show the calculations.
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction