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)^(2) 2^(x) dx=[(2^(x))/(log_(e)2)]_(0)^(1)=(1)/(log 2)*(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^(2))/(2)]_(0)^(1)=(1)/(2)`