Question

Evaluate the definite integral:
int_(1)^(9) 3 sqrt(u) \ du

Answer 1

\[\int\limits\limits_{1}^{9} 3 u ^{1/2} du \[3 \int\limits\limits_{1}^{9} u ^{1/2} du\] \[3[1/(1/2+1)]u^{(1/2+1)}\] evaluated from u=1 to u=9.\[3(2/3)u ^{3/2}\] evaluated from u=1 to u=9. \[3(2/3)(9^{3/2}) - 3(2/3)(1^{3/2})\]\[2(27)-2(1)=54-2=52\]

Answer 2

Oops that first thing was supposed to read:\[\int\limits_{1}^{9}3u ^{1/2} du = 3 \int\limits_{1}^{9} u^{1/2} du\]