Question

Find the area of the region bounded by the curve $y^{2}=x$ and the lines $x=1$, $x=4$ and the $x$ -axis in the first quadrant.

Name: Problem 1, Chapter 8: NCERT Class 12 Part 2 - Math
Uploaded: 2021-10-01T13:59:01-08:00
Duration: 4 min 50 s
Channel: Nisha Gautam
Description: Find the area of the region bounded by the curve y^2=x and the lines x=1, x=4 and the x -axis in the first quadrant.

   Find the area of the region bounded by the curve $y^{2}=x$ and the lines $x=1$, $x=4$ and the $x$ -axis in the first quadrant.

NCERT Class 12 Part 2 - Math

Pawan K. Jain 2006 Edition

Chapter 8, Problem 1

Instant Answer

Solved by Expert Nisha Gautam

10/01/2021

Step 1

The curve $y^{2}=x$ is a parabola with vertex at the origin. The lines $x=1$ and $x=4$ are vertical lines intersecting the $x$-axis at $x=1$ and $x=4$ respectively. The region we are interested in is the area enclosed by the curve and these lines in the first Show more…

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Find the area of the region bounded by the curve $y^{2}=x$ and the lines $x=1$, $x=4$ and the $x$ -axis in the first quadrant.

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Key Concepts

Definite Integration

Definite integration is the mathematical process used to compute the accumulation of quantities, such as area under a curve, within specified limits. It involves setting up and evaluating an integral with upper and lower bounds that correspond to the region of interest.

Expressing Implicit Functions Explicitly

When a curve is given in an implicit form, such as y² = x, it often helps to rewrite it as an explicit function (in this case, y = ?x for the first quadrant) to set up the integral more easily. This transformation allows for direct integration with respect to the chosen variable.

Determining Integration Limits from Region Boundaries

Identifying and establishing the correct integration limits is essential. In problems involving a bounded region, the limits are determined by the points of intersection of the curves and lines that define the region, thereby ensuring that the integral accurately represents the desired area.

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