Question

# intlimits^5_0 {frac{x^{3/2} }{x^{3/2} + (5-x)^{3/2}} } , dx = (a) 0 (b) 5/2 (c) 5 (d) 1/5

Solution

@I =intlimits^5_0 {frac{x^{3/2}dx }{x^{3/2} + (5-x)^{3/2}} } , ...1I=intlimits^5_0 {frac{(5-x)^{3/2}dx }{(5-x^{3/2}+x^{3/2})} } ,...2 2I=intlimits^5_0 {frac{x^{3/2+(5-x)^{3/2}} }{(5-x)^{3/2}+x^{3/2}} } , dx 2I=intlimits^5_0 {dx=[x]^{5}_{0}=5-0=5} , I=frac{5}{2} Option b