JEE Mains · Maths · STD 12 - 8. Application and integration
Let the function,
\(f(x)= \begin{cases}-3 a x^2-2, & x \lt 1 \\ a^2+b x, & x \geqslant 1\end{cases}\)
be differentiable for all \(x \in \mathbf{R}\), where \(\mathbf{a}\gt1, \mathbf{b} \in \mathbf{R}\). If the area of the region enclosed by \(y=f(x)\) and the line \(y=-20\) is \(\alpha+\beta \sqrt{3}, \alpha, \beta \in Z\), then the value of \(\alpha+\beta\) is ________
- A 32
- B 30
- C 34
- D 36
Answer & Solution
Correct Answer
(C) 34
Step-by-step Solution
Detailed explanation
\(f(x)\) is continuous and differentiable \(\begin{aligned} & \text { at } x=1, \mathrm{LHL}=\mathrm{RHL}, \mathrm{LHD}=\mathrm{RHD} \\ & -3 a-2=a^2+b,-6 a=b \\ & a=2 ; b=-12 \\ & f(x)=\left\{\begin{array}{cc} -6 x^2-2, & x Area…
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