Verified answer

∫[1,4] 2x^(-3/2) dx= 2x^(-3/2+1)/(-3/2+1) |[1,4]= -4/√x |[1,4]= -4/√4 -(-4/√1)=2

http://www.wolframalpha.com/input/?i=%E2%88%AB%5B1...

4 ?2x?(x^2+9) dx 0 4 =?(x^2+9)^a million/2 2xdx 0 2xdx is the spinoff of (x^2+9) so quintessential is two/3 (x^2+9)^3/2 now replace x with 4 and then 0 giving 2/3{(sixteen+9)^3/2 -(0+9)^3/2} =2/3{25.5 -9.3} =2/3{one hundred twenty five-27} =(2/3)(ninety 8 =196/3

integral (1 to 4) [ 2x^(-3/2) ] dx

. . . integral = 1 / (-1/2) * 2x^(-1/2) = - 2 * 2x^(-1/2) = - 4 / sqrt(x)

- 4 / sqrt(4) - (- 4 / sqrt(1) )

-4 / 2 + 4 / 1

- 2 + 4 = 2 <=====