Question

# If $$\displaystyle \int _{ a }^{ b }{ { x }^{ 3 } } dx=0$$ and $$\displaystyle \int _{ a }^{ b }{ { x }^{ 2 }dx } =\cfrac { 2 }{ 3 }$$, then what are the values of $$a$$ and $$b$$ respectively?

A
1,1
B
1,1
C
0,0
D
2,2

Solution

## The correct option is A $$-1,1$$from given equation , we can get       $$b^4-a^4=0\Rightarrow (b-a)(b+a)(b^2+a^2)=0$$...............(1)and $$\dfrac{b^3-a^3}3=\dfrac23\Rightarrow b^3-a^3=2\Rightarrow (b-a)(b^2+ab+a^2)=2$$...............(2)From (2) we can see that $$(b-a)$$ is not equal to 0 and $$(b^2+a^2)$$ cannot be zero as it is always positive in (1)so, in (1) we can see that $$(b+a)=0\Rightarrow a=-b$$Putting $$a=-b$$ in (2)$$2b\cdot b^2=2\Rightarrow b=1\ or\ -1$$so. $$a=-1\ or \ 1$$Therefore, Answer is $$A$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More