integration practice

2]\lim_{b\rightarrow a} \frac{\displaystyle\int_a^b \ln |1+(x-a)(b-x)|dx}{(b-a)^3}

(2)
use l hospital
answer should come

for d first q a bettr way is
multiply n divide by √1-x
nw substitue x=sin@
so ur num is cos^2@ d@
and de is 1-sin@

write num as 1-sin^2@

so ur q basically is( 1+sin@ )d@

jaise aap samjoh just postin a bettr way :P

3]\int_0^{\pi} |a\cos nx+b\sin nx|dx\ (n=1,2,\cdots)

answers

1] -1 + π/2

2] 1/6