Question: Could someone help me, plz? Playing with the integral: (x3 81 -x'dx. (a) Identify which radical we need to consider: Ova? - OVI2 - a2
Could someone help me, plz?


Playing with the integral: (x3 \\81 -x'dx. (a) Identify which radical we need to consider: Ova? - OVI2 - a2 Ova+12 (b) For the radical that we have, which trig substitution matches the radical? Or = sin(810) Ou = cos(81x) Ou = sin(81x) Ou = tan(81x) Or = tan(810) (c) Perform the trig substitution and simplify the radical. Write the new integral? do (note: type "theta" to get @) (d) Because we have an odd power for sin(@) and an even power for cos(0), we split up the sin"(@) into sin"(0)sin(0). Then, we replace sin?(0) with 1 - cos?(@) and multiply the cosines. This will gives us the rewritten integral: 0 95 (cos*(0) - cos (0)) sin(0) de /95 (sin ?(0) - sin* (8)) cos(0)de 0 /35 (cos?(@) - cos*(0)) sin(0) de of as (sin ? (0) - sin*(0) ) cos (@) de (d) Peform the appropriate U-substitution to make a new integral: du{e} Integrate and resubstitute to get a function in terms of I9. +6\" [1'] In order to put our answer hack into terms of at, we need to determine what cosf} is in terms of .13. Use the original substitution [from part {b}], develop a triangle and determine what casil] is in terms of x: mm I {g Perform the substitution into the result" In part {e} and develop the answer to the integral in terms of z
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
