integral subscript 2 superscript 3 d x divided by x space equals ? space a n d space integral left parenthesis 1 minus x right parenthesis square root of x d x space equals ?

Asked by Lochana Jayachandran | 5th Oct, 2014, 07:12: PM

Expert Answer:

left parenthesis 1 right parenthesis C o n s i d e r space I equals integral subscript 2 superscript 3 fraction numerator d x over denominator x end fraction equals open square brackets log open parentheses x close parentheses close square brackets subscript 2 superscript 3 equals log open parentheses 3 close parentheses minus log open parentheses 2 close parentheses equals log open parentheses 3 over 2 close parentheses left parenthesis 2 right parenthesis C o n s i d e r space I equals integral open parentheses 1 minus x close parentheses square root of x d x equals integral square root of x d x minus integral x square root of x d x equals fraction numerator x to the power of begin display style 3 over 2 end style end exponent over denominator 3 over 2 end fraction minus fraction numerator x to the power of begin display style 5 over 2 end style end exponent over denominator 5 over 2 end fraction equals fraction numerator 2 x to the power of begin display style 3 over 2 end style end exponent over denominator 3 end fraction minus fraction numerator 2 x to the power of begin display style 5 over 2 end style end exponent over denominator 5 end fraction plus C

Answered by Vimala Ramamurthy | 6th Oct, 2014, 08:57: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.