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$If the area enclosed by curve y = f (x) and y = x^{2} + 2 between the abscissa x = 2 and x = α, α > 2, is$
$(α^{3} - 4 α^{2} + 8) sq. unit. It is known that curve y = f (x) lies below the parabola y = x^{2} + 2$

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detailed solution

Correct option is A

According to the question,α3−4α2+8=∫2α x2+2−f(x)dx Differentiating w.r.t. α on both sides, we get 3α2−8α=α2+2−f(α)∴ f(x)=−2x2+8x+2

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If the area enclosed by curve y=f(x) and y=x2+2 between the abscissa x=2 and x=α,α>2, is α3−4α2+8 sq. unit. It is known that curve y=f(x) lies below the parabola y=x2+2

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material

$If the area enclosed by curve y = f (x) and y = x^{2} + 2 between the abscissa x = 2 and x = α, α > 2, is$
$(α^{3} - 4 α^{2} + 8) sq. unit. It is known that curve y = f (x) lies below the parabola y = x^{2} + 2$