Question

8) Find L10 for f(x) = 22 +3.c +1 from 2 = 1 to 2 = 2.

Answer 1

[" (22 + 3x + 1) da with n = 10 rectangles, using left endpoints. The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a subinterval: b f(x)dx ñ Ax (f(x0) + f(x1) + 2f(x2)+... +f(xn-2) + f(xn-1)) b-a where Ax= n We have that a = 1,b=2, n = 10. 1 Therefore, Ax = 2 – 1 10 10 Divide the interval [1, 2] into n = 10 1 a = subintervals of length Ax 10 11 11 6 6 13 1, 10 105 5' 10 13 7 7 31 3 8 10'5 5' 2 2'5 8 17 17 9 9 19 5'10 105 5' 10 > 18] .

19 2 = b 10 Now, we just evaluate the function at the left endpoints: f (x0) = f(a) = f(1) = 5 = 5 f (x1) = f 21) == ( ) 551 100 = 5.51 151 f (x2) = f (6) = - 6.04 erl 25 659 - = 6.59 100 f (as) = 1 (1) f (xa) =() 179 = = 7.16 25 3 31 f (x5) = f = 7.75 2 4 209 f (x6) = f = - = 8.36 25 17 899 f (x7) = f - 8.99 100

241 - - 9.64 5 25 (73) =s () (1) f (29) = f = 1031 100 - = 10.31 Finally, just sum up the above values and 1 multiply by Δα 10 1 (5 + 5.51 +6.04+...+9.64 10 + 10.31) = 7.535 Answer: 7.535

Therefore, the value of L10 is 7.535

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