Find the following integrals:
(i)`int_(1)^(9)(dx)/(sqrt(x))" "` (ii) `int_(1)^(3)12x^(3)dx " "` (iii) `int_(4)^(16) sqrt(t).dt`

Answer

(i) `4` ,(ii) `240` ,(iii)`(112)/(3)`

Explanation

(i) `underset(1)overset(9)int(dx)/(sqrt(x))=((sqrt(x))/(-1/2+1))_(1)^(4)=2(sqrt(9-sqrt(1)))=4`
(ii)`underset(1)overset(3)int12x^(3)dx=12underset(1)overset(3)intx^(3)dx=12((x^(4))/(4))_(1)^(3)=240`
(iii)`underset(4)overset(16)intsqrt(t)dt=(2)/(3)(t^(3//2))_(4)^(16)=(112)/(3)`