Question

M We assign.net 0 דו HOME -me... Get Hom crk. Grades for De... Homework Watch It Player... HOME mwe 263 zoom CG ... Henniganlina2... Stanford Prison... cantonmity and... Home | Aynal.. https:/bacc.my... 2020-2021 Ac... Cale.. + 20. (-/2 points) DETAILS LARCALC11 4.2.063. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval. MX) = ? + 2, 10, 21 Need Help? Read TN to a Tutor 21. (-/1 Points) DETAILS LARCALC114.3.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral by the limit definition. x x Need Help? Read it Talk to a Tutor 22. (-/1 Points) DETAILS LARCALC11 4.3.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral by the limit definition. [x? x x Need Help? Read It Watch Master It Talk to a Tutor 23. (-11 Points) DETAILS LARCALC11 4.3.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral by the limit definition 1x2 + 3) dx

Answer 1

. 20 f(x) = x²+2 [6, 22 a b m= 4 2-0 = 0 4 width ax=b-a < < =0.5 This end points are H = 0, 2, = 20+02 = 0.5, 22= 21+02= 1 93= 22 +0% = 1.5, Wy= 19+02 = 2 The Mid points are xi 20 +21 oto.5 = 0.25 2 2 0.75 22 - 24+2 B5+1 2 2 23' = 22 + 83 1-25 1+1.5 2 2 1.75 - 99 +24 2 1-5+2 2 Thus F(x)(0.25)2 +2 = 2.0625 flag') - (0.7532+2 (0.75)2+2 = 2.5625 flog) = 4.25)2+2 = 3.5625 Flau) = (1.753 + + 2 5.0625 3

Midpaint Ruele As DX [F(X') +f102') + f183') + Flor'] 0:5 [ 2.0625 +2.5625+ 3-5625+ 5.0629 As 0625 A= 0.5 (13.25) A 6.625 AS. 9 03-21 x doc here a=-8, b=9, f(x)=x is Limit ion, the in by definition intenare! 9 lim { flag ax - ada -8 mos c=1 A2 = ba 9-(-8) = 17 & Ni - ati ax = -8+217 Now 17 flai)

F(Xi) = -8 + Ź (-8 +i 15) E flai) x - i=1 ¿=1 - 24 ti 51 m2 = -24 € () (on) -4512 c=1 m2 13 - 24 3 1 + 51 c=1 E i (=1 m2 1) + si -24 in 00 Soti) 2 m2 f(x)ox - 2u 6+1) + SI 2 Lim E F(Xi).02 lim. [-24 + 52 month") no Myo i=1 = -24.+ 51 lim W11+ Ym) 2 mo D -24 + 51 (1+0) - 48 +51 2 lim { flai) ax moi=1 خانم

0.22 s x3 dor here Q=-4, 6-7 , F 6) = 23 width OX= b-a. = 7-(-7) = 14 limit mo definition Integration 7 -7 * 23 dx = Lime { Fai).ox c=1 too xi= ati sx = - 7+ 6 14 3 flori) = {1+0 19 J (-7)3 + (114.98 - 3.7.1 | (+9+ (-7 til -7+814 n 2 qui - -343 +63 2744 m3 - 343 +1 3 2744 + 2058 ¿- 4116 ;? h8 m2

Nole ? FCG").D2 = 2 (-343 + 274 3 + 2058 2 - 4163) 14 ca ;3 +28.812 = -4802 3.1 + 38,916 c=1 nBy EW!! & W. m2 .2 57,624 C ng cal -4802.00 + 38,416 m (m+1) 9 m4 2 contenuti ya + 28812 02 n (m+1) - 57 624 mmHX2ND) m3 2 lim f(0.09 = lim izl limon - 4802 +38 416 .92 m2 1+You)? m0 DAY 4 +28812 (i+Yo ) n2 2 57624 nom (1+Ym) (2+)? 38 6 11 –480 2 + 38416 (146) +28812 (140) 4 2. - 57624 (1+0) (240)

Sa =? Q = x0 .(.*** 3 lim 89761-gohni + 2996 +3 08h- =