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NDA Application of Integrals questions with solutions

Area under curves. 12 questions from our 2017–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Application of Integrals for JEE Main · Application of Integrals for JEE Advanced

NDA 2025

The area of the region bounded by the curve y=x^3, the line y=8 and the y-axis isNDA 2025 Maths · hard

NDA 2024

The area of the region bounded by the curve y=e^x, the x-axis and the lines x=0 and x=ln 3 isNDA 2024 Maths · medium
The total area enclosed between the curve y=x^3, the x-axis and the lines x=-1 and x=2 isNDA 2024 Maths · hard

NDA 2023

The area, in square units, of the region lying in the first quadrant and enclosed between the curve y=x^3 and the straight line y=x isNDA 2023 Maths · medium

NDA 2021

The area under the curve y=x√(1+x^2 between x=0 and x=1 isNDA 2021 Maths · medium
The area of the region enclosed by the parabola y=x^2 and the line y=2-x isNDA 2021 Maths · hard

NDA 2020

The area of the region bounded by the curves y=|x| and y=6-x^2 isNDA 2020 Maths · medium

NDA 2019

The area of the region enclosed by the curve y=sin x, the y-axis and the line y=1, for 0≤ x≤(π)/(2), isNDA 2019 Maths · medium
The area of the region bounded by the graph of y=|x-1| and the line y=3 isNDA 2019 Maths · medium
The area of the region enclosed by the parabolas y^2=4x and x^2=4y isNDA 2019 Maths · hard

NDA 2017

The area of the region bounded by y=ln x, the x-axis and the line x=e isNDA 2017 Maths · medium
The area enclosed by the curve |x|+|y|=3 isNDA 2017 Maths · easy