Area of the region bounded by curve y²=4x and the X-axis between x=0 and x=1 is : (A) 2/3 (B) 8/3 (C) 3 (D) 4/3

MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2024: question 13

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQApplication of Integrals

Area of the region bounded by curve $y^{2} = 4 x$ and the X-axis between $x = 0$ and $x = 1$ is :

(A) $\frac{2}{3}$
(B) $\frac{8}{3}$
(C)3
(D) $\frac{4}{3}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Use the upper branch $y = 2 x$ .

Hint 2

Integrate from $x = 0$ to $x = 1$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

The region lies above the X-axis, so take $y = 2 x$ : Area $= \int_{0}^{1} 2 x d x$ .
½ mark
$\int_{0}^{1} 2 x d x = \frac{4}{3} [x^{3/2}]_{0}^{1} = \frac{4}{3}$ , option (D).
½ mark

Answer: $\frac{4}{3}$ , option (D)

Where the marks are

Integrates $2 x$ from 0 to 1 (1 mark)

Revise the chapter

Chapter: Application of Integrals (notes, formulas, where marks are lost and every past question)
Topic: Area Involving a Parabola

Practise this chapterBoard-style questions from Application of Integrals, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2024: question 13

Hints

Step-by-step solution

Revise the chapter

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