Find approximate value of integral

\int _{0}^{1/2}\frac {dx}{\sqrt {1-x^{2n}}}

where n≥1

3 Answers

3
msp ·

y don u use binomial approximation for (1-x^{2n})^{-1/2}

11
Tush Watts ·

Ans) 0 < x <1/2
x2n < x2
-x2n > -x2
(1-x2n ) >(1 -x2)
Now, I > √(1-x2n ) > √(1 -x2)
Therefore, I < 1/√(1-x2n ) < 1 / √(1 -x2)

< <

Therefore, (1/2) < I < sin -1 (1/2)

(1/2) < I < ∩/6
or 0.5 < I < 0.52

3
msp ·

tight inequality.nice work.

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