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CBSE Class 12 Math 2009 Solved Paper

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Question : 3 of 29
Marks: +1, -0
If ∫01(3x2+2x+k)\int\limits_{0}^{1}(3x^2+2x+k) dx = 0 , find the value of k.
Solution:  
Given: ∫01(3x2+2x+k)\int\limits_{0}^{1}(3x^2+2x+k) dx =
⇒ [3x33+2x22+kx]01\left[ \frac{3x^3}{3} + \frac{2x^2}{2} + kx \right]_{0}^{1} = 0
⇒ [x3+x2+kx]01\left[ x^3 + x^2 + kx \right]_{0}^{1} = 0
⇒ [1 + 1 + k] = 0
⇒ k = - 2
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