NDA Definite Integrals questions with solutions
Definite integrals and their properties. 23 questions from our 2017–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
NDA 2025
NDA 2024
NDA 2023
- Let f(x)=x for 0≤ x≤1 and f(x)=2-x for 1<x≤2. Then ∫0^2f(x) dx is equal to
- Interpreting as an area, the value of the definite integral ∫0^3√(9-x^2 dx, taken between the limits 0 and 3 of the radius-3 curve, is
- ∫0^3[x] dx, where [x] is the greatest integer function, is equal to
- The value of the definite integral of the function sin ^2xcos x over the symmetric interval from -(π)/(2) to (π)/(2) is
- Consider the following two claims about definite integrals over [0,1]: 1. ∫0^1x dx=∫0^1x^2 dx. 2. ∫0^1x^2 dx=∫0^1(1-x)^2 dx.
NDA 2021
NDA 2020
- The modulus integral ∫-2^3|x-1| dx, which measures the area between the graph and the x-axis, equals
- ∫2^5(√ x)/(√ x+√(7-x)) dx is equal to
- Using the identity connecting tan ^2x and sec ^2x, the value of ∫0^π/4tan ^2x dx is
- Two statements about definite integrals over the interval [0,(π)/(2)] are given below. 1. ∫0^π/2sin x dx=∫0^π/2cos x dx. 2. ∫0^π/2sin ^2x…
NDA 2019
NDA 2017
Other Mathematics topics
Three Dimensional Geometry 48Vector Algebra 60Complex Numbers and Quadratic Equations 35Binomial Theorem 16Sequences and Series 36Quadratic Equations 27Permutations and Combinations 25Statistics 35Probability 27Matrices 37Determinants 13Sets, Relations and Functions 39Binary Number System 11Logarithms 11Inverse Trigonometric Functions 22Trigonometric Functions and Identities 49Trigonometric Equations 16Properties of Triangles 18Heights and Distances 12Straight Lines 43Circles 21Conic Sections 28Limits 23Continuity and Differentiability 16Application of Derivatives 34Derivatives 33Integrals 16Application of Integrals 12Differential Equations 30