Solved: "Find the limit limb→1−∫0bdx1−x2"

Chaya Galloway

Answered question

2021-02-01

Find the limit

lim_{b \to 1^{-}} \int_{0}^{b} \frac{d x}{\sqrt{1 - x^{2}}}

Dora

Skilled2021-02-02Added 98 answers

Given:

lim_{b \to 1^{-}} \int_{0}^{b} \frac{d x}{\sqrt{1 - x^{2}}}

First, we will find integration:

lim_{b \to 1^{-}} \int_{0}^{b} \frac{d x}{\sqrt{1 - x^{2}}}

This is an standart integral:

= [\arcsin (x)]_{0}^{b}

= [\arcsin (b) - \arcsin (0)]

= \arcsin (b)

Now, find the limit:

lim_{b \to 1^{-}} \arcsin (b)

Plug b=1

= \arcsin (1)

= \frac{π}{2}

lim_{b \to 1^{-}} \int_{0}^{b} \frac{d x}{\sqrt{1 - x^{2}}} = \frac{π}{2}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?