Find the limit lim_{brightarrow1^-}int_0^bfrac{dx}{sqrt{1-x^2}}

Chaya Galloway 2021-02-01 Answered
Find the limit
limb10bdx1x2
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Expert Answer

Dora
Answered 2021-02-02 Author has 98 answers
Given:
limb10bdx1x2
First, we will find integration:
limb10bdx1x2
This is an standart integral:
=[arcsin(x)]0b
=[arcsin(b)arcsin(0)]
=arcsin(b)
Now, find the limit:
limb1arcsin(b)
Plug b=1
=arcsin(1)
=π2
limb10bdx1x2=π2
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