Question

Use n = 4 to approximate the value of the integral by the following methods: (a) the trapezoidal rule, and (b) Simpson's rule. (c) Find the exact value by integration. 1 - x 3x e dx 0 (a) Use the trapezoidal rule to approximate the integral. 1 Joxe -x² dx~ 0 (Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.)

Answer 1

Soll: (a) Given that n = 4 3re da We know Trapezoidal rule (F(onda F(40) + f(un)) +2( f(x0) + f(x2) + f(43) ---) an b 2 go h= bra 44 - 1-0 4 J 4 Divide interval Co, I] into n=4 length ha Q-0, t. 3,1-b 3x ex dx § (CF170) + f(14) ) + 2 ($(4) + f(12) +f()) = 310) e-001? - 2x3x4. e-(+)2 1.4 091195 f(%o) = f(a) – flo) 2 f(x) = 2464) 9 (19) = 2115) 24 (93) = 2 +1}) = 2x3x3 e-tic) - 2.3364023 2x3x4.e-14) - 2.5640227 1:1036383 f(y) =f(b) = +11) = 3 e-) (e-x² de = is (0 + 1.1036393) + (1.4091195 +2.336402372.5640227) 0.9266478 Warni - 0.92665 Ang CSscanned with Cam Seatter