1
1
(b-a) / (1 +b²) < arctan(b) - arctan(a) < (b-a) / (1 +a²) if a<b
also show that (pi/4) + (3/25) < arctan(4/3) < (pi/4) + (1/6)
----------------------------------------------
-----------------------------------------------
use f(x) = arctanx and use a<c<b to manipulate into the given expression
for the second part since pi/4 = arctan(1) use a = 1 and b = 4/3, the 3/25 and 1/6 will come
form (b-a) / (1 +b²) and (b-a) / (1 +a²)
answer and some steps are given below
================
* *
================
other problems on applications of integration like area ,volume etc
integration formulae
problems on integration
**
list of formulae and notes on some math topics
collection of revision questions
formulae on sequences and series
(trig. formulae)
(integration formulae)
(other math problems without classification) or problem index
(formulae on differentiation)
rbmix.com
tags:integral, completion of square, trigonometry, math, homework help, tutor