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NDA Integrals questions with solutions

Indefinite integrals and techniques of integration. 16 questions from our 2017–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

NDA 2025

Using the substitution u=x^3, the value of ∫0^1x^2e^x^3 dx isNDA 2025 Maths · medium
Find the indefinite integral: ∫(sin x)/(1+cos ^2x) dxNDA 2025 Maths · hard
Find the indefinite integral: ∫(dx)/(e^x+e^-x)NDA 2025 Maths · hard
Using the substitution u=1+sin x, the value of ∫0^π/2(cos x)/(1+sin x) dx isNDA 2025 Maths · easy

NDA 2024

∫(dx)/(xln x) is equal to (where C is a constant of integration)NDA 2024 Maths · medium
∫ e^x(sin x+cos x) dx is equal to (where C is a constant of integration)NDA 2024 Maths · hard

NDA 2023

Using the substitution u=1+x^2, the indefinite integral of x√(1+x^2 with respect to x isNDA 2023 Maths · medium

NDA 2021

The antiderivative of (x+1)/(x^2+2x+3) with respect to x isNDA 2021 Maths · medium

NDA 2020

The value of the definite integral ∫0^1tan ^-1x dx, found by parts, isNDA 2020 Maths · medium
The integral ∫0^1x^2ln x dx converges at the lower limit, and its value isNDA 2020 Maths · medium
Using integration by parts twice, the definite integral ∫1^e(ln x)^2 dx evaluates toNDA 2020 Maths · hard

NDA 2019

A student simplifies the denominator of (1)/(1+cos x) with a half-angle identity before integrating it with respect to x. The antiderivative obtained…NDA 2019 Maths · medium
Using the substitution u=ln x, the integral ∫(cos (ln x))/(x) dx is evaluated asNDA 2019 Maths · easy

NDA 2018

∫0^3(dx)/(√(9-x^2) equalsNDA 2018 Maths · easy

NDA 2017

∫√(x) ln x dx is equal toNDA 2017 Maths · hard
∫(dx)/(√(9-4x^2) is equal toNDA 2017 Maths · medium