Question

please show all work and dont forget to evaluate the intefral

Use a Taylor series to approximate the following definite integral. Retain as many terms as needed to ensure the error is less than 10-4. 0.33 S s in (1+x2) dx 0 Rewrite the given integral using a Taylor series and simplify the result. Choose the correct answer below. 0.33 0.33 x4 x4 OA X- x² ² 2! 3! + dx B. X- x² x² 2 3 + +.. dx 4! 4 0 0 0.33 0.33 X4 X4 OC. +2 Xo X² 3! 4! + dx OD. +2 X8 4! X6 3! + + ... dx 2! 2! 0 0 S S S s S S S S 0.33 0.33 x2 x6 X8 O E. X + X3 3! + + x" 4! + .. dx OF. x2 + +... dx 2! 2 3 4 0 0 0.33 0.33 x2 x4 X X8 OG X + x3 3 XA 4 + + ... он. + + + + + dx 2 3 4 0 0 Evaluate the integral such that the error is less than 10-4

Answer 1

이 0,33 f ln (1+x2) da using Taylor series of ln (1+2) at x = 0 since in (1+2) = x - x + 23 - 24 tots - put a x² en (1+2) = x² 4 - 1 + x 3 0.33 ln (1+x2) da 033 (2-3 +x6 O ) obe option F) is correct. G sc