Which of the following is true ?

Options

A. ` int _(0)^(1) e^(x) dx = e`
B. ` int _(0)^(1) 2^(x) dx = log 2`
C. `int _(0)^(1) sqrt(x) dx = 2/3`
D. ` int _(0)^(1) x dx = 1/3`

Answer

C

Explanation

(a) `int_(0)^(1)e^(x)dx=[e^(x)]_(0)^(1)=e-1`
(b) `int_(0)^(1)2^(x)dx=[(2^(x))/(log_(e )2)]_(0)^(1)=(1)/(log2).(2-2^(0))=(1)/(log 2)`
(c ) `int_(0)^(1) sqrt(x)dx = [(x^(3//2))/(3//2)]_(0)^(1)=(2)/(3)`
(d) `int_(0)^(1) x dx = [(x^(x^(2))/(2))]_(0)^(1)=(1)/(2)`