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  • Solve this problem - Let. If I is minimum then the ordered pair (a,b) is: - Integral Calculus - JEE Main

Let I = \int_{a}^{b}(x^{4}-2x^{2})dx. If I is minimum then the ordered pair (a,b) is:

  • Option 1)

     

    (0,\sqrt2)

  • Option 2)

     

    (-\sqrt2,0)

  • Option 3)

    (\sqrt2,-\sqrt2)

  • Option 4)

     

    (-\sqrt2,\sqrt2)

Answers (1)

best_answer

 

lower and upper limit -

\int_{a}^{b}f\left ( x \right )dx= \left ( F\left ( x \right ) \right )_{a}^{b}

                = F\left ( b \right )-F\left ( a \right )

 

- wherein

Where a is lower and b is upper limit.

 

  f(x) = x4 -2x2

Plot the curve.

When the graph of f(x) lie below x-axis , value of integral will be negative.

So, ordered pair of (a,b) is \left ( -\sqrt{2} , \sqrt{2} \right ) .

 


Option 1)

 

(0,\sqrt2)

Option 2)

 

(-\sqrt2,0)

Option 3)

(\sqrt2,-\sqrt2)

Option 4)

 

(-\sqrt2,\sqrt2)
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