Start learning →

JEE Advanced Integrals and Applications — practice questions — page 3

Explore 90 free Integrals and Applications questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Integrals and Applications with Quill →

Integrals and Applications questions and exercises with answers

Showing questions 61–90 of 90.

Flip and pair: term with meaningRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →True or false: reading the notationRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →True or false: what the constant meansRead the answer and worked solution →Tap every true statement about integrationRead the answer and worked solution →To evaluate $\int x\cos x\, dx$, the best technique is:Read the answer and worked solution →By the Fundamental Theorem of Calculus, ∫_0^2 (3x² + 2x) dx equals:Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →The integral $\int x^3\, dx$ equals:Read the answer and worked solution →The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:Read the answer and worked solution →The improper integral ∫_1^∞ (1/x²) dx evaluates to:Read the answer and worked solution →$\displaystyle\int x^n\,dx$ (where $n \ne -1$) equals:Read the answer and worked solution →The integral ∫ x^n dx (for n ≠ -1) equals:Read the answer and worked solution →Using integration by parts, $\displaystyle\int x e^x\,dx$ equals:Read the answer and worked solution →To solve the homogeneous differential equation $\dfrac{dy}{dx} = \dfrac{x^2 + y^2}{xy}$, the appropriate substitution is:Read the answer and worked solution →Using partial fractions, $\displaystyle\int \dfrac{1}{(x-1)(x-2)}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{x^2 - a^2}\,dx$ (with $|x| > a > 0$) equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{\sqrt{1 - x^2}}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \sec^2 x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \log x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:Read the answer and worked solution →Using the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:Read the answer and worked solution →Properties in useRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Which process is being described?Read the answer and worked solution →The number of arbitrary constants in the general solution of a differential equation of order $n$ is:Read the answer and worked solution →True or false: calculusRead the answer and worked solution →The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2$ is:Read the answer and worked solution →

Worked practice questions

Flip and pair: term with meaning

Read exercise and reference answers
Matching pairs
  1. A
    Integration
    B
    the inverse of differentiation
  2. A
    Indefinite integral
    B
    carries a constant of integration
  3. A
    General integral
    B
    another name for the indefinite integral
  4. A
    C
    B
    the constant of integration
The chapter's vocabulary. Source: syllabus Maths, Ch 7 Integrals.

Open this exercise →

Spot the one that does not belong

Read exercise and reference answers
Questions
  1. Items
    1. Constant of integration
    2. Derivative
    3. Indefinite integral
    Odd item
    Derivative
  2. Items
    1. Sums split
    2. Constants come outside
    3. Products split
    Odd item
    Products split
  3. Items
    1. Rate of change
    2. Integration
    3. Antiderivative
    Odd item
    Rate of change
One item is a differentiation idea. Source: syllabus Maths, Ch 7 Integrals.

Open this exercise →

True or false: reading the notation

Read exercise and reference answers
Questions
  1. Statement is true
    Yes
    Statement
    The integral sign indicates integration.
  2. Statement is true
    Yes
    Statement
    The dx names the variable being integrated over.
  3. Statement is true
    Yes
    Statement
    The C at the end is arbitrary.
  4. Statement is true
    Yes
    Statement
    Two correct answers to one indefinite integral may look different.
  5. Statement is true
    No
    Statement
    They must then differ by more than a constant.
What each part of the expression means. Source: syllabus Maths, Ch 7 Integrals.

Open this exercise →

How to practise

  1. Choose a Integrals and Applications question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Integrals and Applications practice for JEE Advanced. Read explanations as you go. No signup form needed to start.

Practise Integrals and Applications →

More Mathematics topics

Vector Algebra and 3D GeometryStatistics and ProbabilityContinuity, Differentiability & DerivativesMatrices and DeterminantsRelations, Functions & Inverse TrigonometryStraight Lines and Conic SectionsDeterminantsDifferential Equations