x2n+1 E(-1)". (2n + 1)! The Maclaurin Series of sin x is sin x = for all x E R. n=0 1. Express the integral x° sin x dx as a series of constant terms. 2. Find the 5th degree Maclaurin polynomial for...

I've been trying to answer these two for hours. Pls help me with both since they are connected and actually under 1 item. I also included reference for more convenience on your part. Thank you and will upvote!

Extracted text: x2n+1 E(-1)". (2n + 1)! The Maclaurin Series of sin x is sin x = for all x E R. n=0 1. Express the integral x° sin x dx as a series of constant terms. 2. Find the 5th degree Maclaurin polynomial for sin(2x) and use it to approximate the value of sin(0.02). (Do not simplify.)


Extracted text: x" = 1 +x + x² + x³ + • ·. R= 1 e Σ 1 + + 2! 1! R=00 ... 3! x2a+1 sin x= E(-1)ª. R= 0 = X - 3! + 7! - (2n + 1)! 5! n-0 x* cos x= E(-1)-. 1 2! R= 0 %D ... (2n)! 4! 6! n-0 19 x2a+1 tan 'x= E(-1)“- = X R=1 %3D 2n+1 x2 In(1 + x) = E(-1)ª-1 R=1 = X- - + +... - 2 3 4 (1 + x)* = E (* k(k – 1) -x² + 2! k(k – 1)(k – 2) 3 +... x" = 1 + kx + R= 1 3! +