find derivative of integral( t sint dt) upper limit 1+2x, lower limit 1-2x

Question

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Answer 1

Just use Leibniz's Rule:

d/dx(∫[1-2x,1+2x] t sint dt)
= (1+2x)sin(1+2x)(2) - (1-2x)sin(1-2x)(-2)
= 2(1+2x)sin(1+2x) + 2(1-2x)sin(1-2x)