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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Area Under Curves

NDA 2022 · Mathematics · Area Under Curves

What is the area included in the first quadrant between the curves...

What is the area included in the first quadrant between the curves y=xy=x and y=x3y=x^3 ?

Options

  1. A18\frac{1}{8} square unit
  2. B14\frac{1}{4} square unit
  3. C12\frac{1}{2} square unit
  4. D1 square unit

Correct answer

B. 14\frac{1}{4} square unit

Step-by-step solution

y=xy=x...(i) y=x3y=x^3..(ii) Solving equations (i) and (ii) we get ∴\therefore Required area =∫01xdx−∫01x3dx=[x22]01−[x44]01=12−14=14=\int_0^1 x d x-\int_0^1 x^3 d x=\left[\frac{x^2}{2}\right]_0^1-\left[\frac{x^4}{4}\right]_0^1=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}
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