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If f(x) be a quadratic polynomial such that f(0) = 2, f ¢(0) = -3 and f ²(0) = 4 then \int_{-1}^{1}f(x)dx is equal to

  • Option 1)

    -3

  • Option 2)

    16/3

  • Option 3)

    0

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

Properties of Definite Integration -

If f(x) is an odd function of x then integral of the function from -a to a is ZERO

\int_{-a}^{a}f(x)dx=0
 

- wherein

Check

Odd function f(-x)= -f(x)

 

 

Let f(x) = ax2 + bx + c

                        \     f ¢(x) = 2ax + b, f ²(x) = 2a

                        \   2 = c, -3 = b, 4 = 2a (from the question)

                        \   f (x) = 2x2 - 3x + 2

                        \ \int_{-1}^{1}f(x)dx=\int_{-1}^{1}\left ( 2x^{2}-3x+2 \right )dx=\left [ \frac{2x^{3}}{3} -\frac{3x^{2}}{2}+2x\right ]_{-1}^{1}= 16/3

 


Option 1)

-3

Option 2)

16/3

Option 3)

0

Option 4)

none of these

Posted by

gaurav

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