Question

2. a) Find an approximation to the integral (%(x2 - 4x) dx using a Riemann sum with right endpoints and n=4. b-a and x,-a +Ax. Use this to b) Using the definition ()dx = lim Žf(x7)Ar, where Ar = ? evaluate 1, (x2 - 4x) dx

Answer 1

(2) @ soli- from the given data we havez 2 Find approximatlon to the integral | (2?–48)dx using Riemann som with right end points and n=4 2 → 8 (3²-ux) dx ,n=4 D Riemann sum b t + f(2n-1) +F(An)] f f(x) dx - Ax [1441) + f(42) + F(43) + a b-a 2-0 = AX -10 2 n 4 - 2 C - 2 - - u 7 Y = -1.75 - -3 The reght endpoints of the subinterval [0, 2] of length Dx = 3,1,3,2 F(x) = f() - (11-4(:) - f(x2) = f(1) = (0)-1(1) f(as) = f() - ()-(1) - 4-6 f(x4) = f(2) (2)2-1(2) į (x2-yx) dx = { [ -15-3-3.15–4] ah -15 こ = -3.75 V 4 - 8 - 4 31510 -6.25 2 f (x²-ux) dx = -6.825 -6.25 (z*=4) dx

6 Soli- from the given daba we have n lim using the definition of floodx= į f(x4) Ac , where x>0 il and X; = a +i Sx i use this to evaluate S (x=-ux)dx 2 b-a Ax= n n be frx) dx lim E fro;) i=1 no 2 p (x²-4x) dx 0 b-a 2-0 Ax= 1) 11 ools n n n 0 so = atida ot २ = 2i n n Lim flas) = (*)*-4 (3.) - anti-() - (-) ["(*- ) ( - ) f (x²-4x) dx こ E n> 9 = 1 n lim 8 sloo I MS no n lim nin+1) (2n+1) 2nn+) sloo no En 2 an lim 8 nin+1)(2n +1) an (n+1) [ nya on 3 2n2 lim Anth t2n+) lim n²tn 3 6 2 nto na nto 8 11 = 응 (2) 8 16 3 6 2 f (x²-ys) dx - 16 3 o If you Impress with answer. please please give me TAKA