QJEEM21Mae851: JEE Main 2021 Mathematics - Class 12 JEEM21Mae851 Solution: Let a and b respectively be the points of local maximum and…

Question

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Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x³

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3x²

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12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______________.

Accepted Answer

f'(x) = 6x²

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6x

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12 = 6(x

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2) (x + 1)

Point = (2,

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20) & (

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1, 7)

A = \int_{- 1}^{0} (2 x^{3} - 3 x^{2} - 12 x) d x + \int_{0}^{2} (12 x + 3 x^{2} - 2 x^{3}) d x

A = {(\frac{x^{4}}{2} - x^{3} - 6 x^{2})}_{- 1}^{0} + {(6 x^{2} + x^{3} - \frac{x^{4}}{2})}_{0}^{2}

4A = 114

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