Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Area Under Curves

NDA 2019 · Mathematics · Area Under Curves

What is the area of the region enclosed between the curve y^2=2 x...

What is the area of the region enclosed between the curve y2=2xy^2=2 x and the straight line y=xy=x ?

Options

  1. A23\frac{2}{3} square units
  2. B43\frac{4}{3} square units
  3. C13\frac{1}{3} square units
  4. D1 square units

Correct answer

A. 23\frac{2}{3} square units

Step-by-step solution

y2=2x,y=xy^2=2 x, y=x∵y2=2xy=x⇒x2=2x⇒x=0,2∴ Area =∫02(2x−x)⋅dx=[2⋅x3−32−x22]02=(43/2−42)−0=83−2=23 sq. unit \begin{aligned} & \because y^2=2 x & y=x \\ & \Rightarrow x^2=2 x \\ & \Rightarrow x=0,2 \\ & \therefore \text{ Area }=\int_0^2(\sqrt{2 x}-x) \cdot d x \\ & =\left[\frac{\sqrt{2} \cdot \sqrt{x^3}}{-\frac{3}{2}}-\frac{x^2}{2}\right]_0^2 \\ & =\left(\frac{4}{3 / 2}-\frac{4}{2}\right)-0 \\ & =\frac{8}{3}-2=\frac{2}{3} \text{ sq. unit }\end{aligned}$$
Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Let k be the area between the curve y= x and x-axis in the interval [0,(π)/(4)]… NDA 2026Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the area bounded by the… NDA 2026Passage: Let k be the area between the curve y= x and x-axis in the interval [0,(π)/(4)]… NDA 2026Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| .… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = x^2… NDA 2025For the following three (03) items: Consider the function f(x) = x|x| . What is the area… NDA 2025Consider the following for the two (02) items that follow: The slope of the tangent to… NDA 2025What is the area of the region bounded by |x| ≤ 2k and |y| ≤ k , where k is a positive… NDA 2025Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [·]… NDA 2025Paragraph: The area bounded by the parabola y^2=k x and the line x=k , where k > 0 , is… NDA 2024The circle x^2+y^2-2 x=0 is partitioned by line y=x in two segments. Let A_1, A_2 be the… NDA 2024Paragraph: The area bounded by the parabola y^2=k x and the line x=k , where k > 0 , is… NDA 2024The circle x^2+y^2-2 x=0 is partitioned by line y=x in two segments. Let A_1, A_2 be the… NDA 2024What is the area between the curve f(x)=x|x| and x -axis for x ∈[-1,1] ? NDA 2023For what value of m with m < 0 , is the area bounded by the lines y=x, y=m x and x=2… NDA 2023What is the area of the region (in the first quadrant) bounded by y= 1-x^2 , y=x and y=0 ? NDA 2022 Full Area Under Curves list Area Under Curves JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs