Integral Calculus Question 340
Question: $ \int_{{}}^{{}}{(1-x^{2})\log x\ dx=} $
[DSSE 1982]
Options:
A) $ ( x-\frac{x^{3}}{3} )\log x-( x-\frac{x^{3}}{9} )+c $
B) $ ( x-\frac{x^{3}}{3} )\log x+( x-\frac{x^{3}}{9} )+c $
C) $ ( x+\frac{x^{3}}{3} )\log x+( x+\frac{x^{3}}{9} )+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{(1-x^{2})\log x,dx}=\int_{{}}^{{}}{\log x,dx}-\int_{{}}^{{}}{x^{2}\log x,dx} $ $ =x(\log x-1)-\frac{x^{3}\log x}{3}+\frac{x^{3}}{9}+c $ $ =( x-\frac{x^{3}}{3} )\log x-( x-\frac{x^{3}}{9} )+c. $
BETA
