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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Area Under Curves

NTA Abhyas 2020 · Mathematics · Area Under Curves

The positive value of parameter a for which the area bounded by...

The positive value of parameter aa for which the area bounded by parabolas y=x−ax2y = x - a{x}^{2} and ay=x2ay = {x}^{2} attains the maximum value is

Correct answer

1

Step-by-step solution

Points of intersection are at x=0,a1+a2x = 0, \dfrac{a}{1 + {a}^{2}}
Area = \mathop{∫}_{0}^{\dfrac{a}{1 + {a}^{2}}}\left(x - a{x}^{2} - \dfrac{{x}^{2}}{a}\right)dx<br/><br />= \dfrac{1}{6} . \dfrac{1}{{\left(a + \dfrac{1}{a}\right)}^{2}}<br/>Hence,areaismaximumwhen<br />Hence, area is maximum whena = 1 ∵ a + \dfrac{1}{a} \ge 2
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