If p=78 then what should be the value of n∫1g(x)xp+1dx
when g(x)=xlogxorg(x)=xlogx?
Wondering which way to proceed?
- an algebraic substitution,
- partial fractions,
- integration by parts, or
- reduction formulae.
Please don't suggest something like ("Learn basic Calculus first" etc).
Kindly help by solving if possible because I'm out of touch with calculus for nearly 15 yrs.
Answer
g(x)xp+1=xlogxxp+1=logxxp
By parts:
u=1xp,u′=−pxp+1v′=logx,v=xlogx−x
Thus:
n∫1logxxpdx=(logxxp−1−1xp−1)|n1+pn∫1logxxpdx−pn∫11xpdx……
No comments:
Post a Comment