Let [ I = _a^b ( x^4 - 2x^2 ) dx.] If I is minimum then the ordered pair (a, b) is -

Question

Let  $${\rm I} = \int\limits_a^b {\left( {{x^4} - 2{x^2}} \right)} dx.$$  If I is minimum then the ordered pair (a, b) is -

Accepted Answer

Let f(x) = x2(x2 - 2)

As long as f(x) lie below the x-axis, define integral will remain negative,

so correct value of (a, b) is (- $$\sqrt 2 $$, $$\sqrt 2 $$) for minimum of I

Solutions · 1