If `int_(a)^(b)x^(3) dx = 0` and `int_(a)^(b) x^(2) dx = 2/3` then what are the values of a and b respectively ?

Options

A. `-1,1`
B. `1,1`
C. `0,0`
D. `2,-2`

Answer

A

Explanation

`{:(int_(a)^(b)x^(3).dx=0),(rArr ((x^(4))/(4))_(a)^(b)=0),(rArrb^(4)-a^(4)=0),(rArr (b^(2)-a^(2))(b^(2)+a^(2))=0),(rArr (b+a)(b-a)=0 ("or") b^(2)+a^(2) = 0),(rArr b = -a ("or") a = b ("or") b^(2) + a^(2) = 0):}|:(int_(a)^(b) x^(2).dx=(2)/(3)),(((x^(3))/(3))_(a)^(b)=2/3),(rArr b^(3) - a^(3) = 2),(" Since " b = -a),(rArr b^(3) - (-b^(3))=2),(rArr 2b^(3)=2),(rArr b^(3)=1),(rArrb=1a=-1):}`