Let the function, f(x)={\\begin{array}{cc}-3 a x^2-2{ & \\\\end{array} , x< 1 ; a^2+b x{, } , x \geq 1 } be differentiable for all x \in R, where a>1, b \in 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 \_\_\_\_ . [22 Jan 2025 Shift 1]

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 25 of 69

Marks: +1, -0

Let the function,
f(x)={

−3ax2−2,‌	x<1
a2+bx,‌	x≥1

be differentiable for all x∈R, where a>1,b∈R. If the area of the region enclosed by y=f(x) and the line y=−20 is α+β√3,α,β∈Z, then the value of α+β is ____ .

[22 Jan 2025 Shift 1]

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