00:01
We are given in the question that f of x is equal to integral from 0 to x sine 70 squared t and in part a we have to find the macloren polynomial for fopax so we know that mcclorine polynomial of sine x is given as sine x is equal to x minus x cube divided by 3 factorial plus x raised to power 5 divided by 5 factorial minus x raised to power 7 divided by 7 factorial and so on so replacing x by 70 square we get sign 70 square is equal to 70 square minus 70 square cube divided by 3 factorial plus 70 square raised to power 5 divided by 5 factorial minus 70 square raised to power 7 divided by 7 factorial and so on.
01:30
So, we will be getting 70 square minus 7 cube multiplied t -raise to power 6 divided by 3 factorial plus 7 -raise to power 5 multiplied t -raise to power 10 divided by 5 factorial minus 7 -raise to power 7 multiplied t -raise to power 14 divided by 7 factorial and so on.
02:01
So, integrating both sides, we get integration from 0 to x, sign 70 square dt is equal to integration from 0 to x, 7t square minus 7 cube t raised to power 6 divided by 3 factorial, plus 7 r.
02:29
5, multiply t raised to power 10 divided by 5 factorial, minus 7 r.
02:36
7, t raised to power 14 divided by 7 factorial, and so on with respect to dt.
02:44
So, neglecting all the terms of degree greater than 7, we get 7 divided by 3 x cube minus 7 x raised to power 7 divided by 3 factorial multiply 7.
03:17
So we have 7 divided by 3 x cube minus 49 divided by 6 multiply x raised to power 7...