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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 area bounded by the curve y = (1)/(2)x^ 2 , x -axis and x = 2 is

The area bounded by the curve

y = \dfrac{1}{2}x^{2}

,

x

-axis and

x = 2

is

The area bounded by the curve y = (1)/(2)x^ 2 , x -axis and x = 2 is

Options

A $\dfrac{1}{3}squnit$
B $\dfrac{2}{3}squnit$
C $1squnit$
D $\dfrac{4}{3}squnit$

Correct answer

D. $\dfrac{4}{3}squnit$

Step-by-step solution

Required area

= {∫}_{0}^{2}ydx

The area bounded by the curve y = (1)/(2)x^ 2 , x -axis and x = 2 is

= {∫}_{0}^{2}\dfrac{x^{2}}{2}dx = {\left[\dfrac{x^{3}}{6}\right]}_{0}^{2} = \dfrac{4}{3}squnit

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