Step by step solution to "Evaluate the integral. ∫51234sin⁡h−1xx2+1dx"

Ann Tice

Answered question

2021-11-08

Evaluate the integral.

\int_{\frac{5}{12}}^{\frac{3}{4}} \frac{{\sin h}^{- 1} x}{\sqrt{x^{2} + 1}} d x

Theirl1972

Beginner2021-11-09Added 22 answers

Step 1
Definition used -
Integration by substitution -

\int f (g (x)) \cdot g^{'} (x) d x

Taking u = g(x)
The integration will be -

\int f (u) d u

Step 2
Given -

\int_{\frac{5}{12}}^{\frac{3}{4}} \frac{{\sin h}^{- 1} x}{\sqrt{x^{2} + 1}} d x

\int \frac{{\sin h}^{- 1} x}{\sqrt{x^{2} + 1}} d x

Let

u = {\sin h}^{- 1} x

d u = \frac{1}{\sqrt{1 + x^{2}}} d x

\int u d u = \frac{u^{2}}{2}

= \frac{1}{2} {({({\sin h}^{- 1} x)}^{2})}_{\frac{5}{12}}^{\frac{3}{4}}

= \frac{1}{2} ({(0.69314718055995)}^{2} - {(0.40546510810816)}^{2}) = 0.1582

Answer

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