Question

Use the Midpoint Rule with n = 5 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. (Round your answer to two decimal places.)

13. [-75.55 Points] DETAILS LARAPCALC10 5.6.012. MY NOTES Use the Midpoint Rule with n = 5 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. (Round your answer to two decimal places.) Function Interval f(x) = (x3 + 9)3/4 [-1, 1]

Answer 1

3th Let fox) = (x3 +9) NE EL 1 By using the mid-point Rule, the area of the region bounded by graph of font x-axis the internal E1, 11 aver Areea ū sx ff2e X) + f ( x11 3x) + f(x2+xy ) + f(x9 1:24) + foto) Here 1-(-1) = 2 Ax= b-a nh S divide the internal into s subintewals with length Ana 2 ao = Xo = -2, 8 = -3 X2-5 ga's *} xs= b = 1 Then the value of f is 125 3/4 f (-2) (5585) 125 33 ff Mo +24) - f -- + Cys)) - 4*) - (5308) f(31130) -- f (03) + -)) $420139) --H3)+(!)) f(+3+34) = f(): (?). f(3) = (soos $44*35) = f() (1)) --f(1) = 314 125 (5945) 344 125

Hence, 1 314 Area > 2 [ (53042 [ (53063", Cases + 33+ (5665) 125 Area 10.3910229392 Thus Area 10.39