Find value of a

\lim_{x\rightarrow 0}\int_{0}^{x}{\frac{t^2dt}{(x-sinx)\sqrt{a+t}}}=1

1 Answers

See
1/(x-sinx) ₀âˆ«^x t²dt/âˆša+t

a+t =b²
2bdb/dt=1
dt= 2bdb

1/(x-sinx)âˆ«(b²-a)²*2bdb/b
[1/(x-sinx)]2âˆ«(b²-a)²db
[1/(x-sinx)]2[b⁵/5 + a²b -2ab³/3]

b is integrated from a+x to a

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