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If a curve $y = a \sqrt{x} + b x$ passes through the point ( 1·, 2) and the area bounded by the curve, line x = 4 and x-axis is 8 , then

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a = 3

a = -3

b = 1

b = -1

answer is A, D.

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Detailed Solution

$y = a \sqrt{x} + b x x = 4, y = 0 \begin{array}{l} \Rightarrow y = a + b = 2 \\ \Rightarrow a + b = 2 \end{array}$

given $\int_{0}^{4} (a \sqrt{x} + b x) d x = 8$

$= {[\frac{a (\sqrt{x})^{3}}{3} x + \frac{b x^{2}}{2}]}_{0}^{4} = 8 \Rightarrow \frac{2 a}{3} + b = 1$

$\Rightarrow 2 a + 3 b = 3$

from (1) and (2), we get $a = 3, b = - 1$

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