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Indian Navy MR Application of Integrals — practice questions — page 2

Explore 45 free Application of Integrals questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Application of Integrals questions and exercises with answers

Showing questions 31–45 of 45.

Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: check an indefinite integralRead the answer and worked solution →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 →Definite or indefinite?Read the answer and worked solution →Reading the definitions backRead the answer and worked solution →Complete the linearity rulesRead the answer and worked solution →Which process is being described?Read the answer and worked solution →True or false: what the constant meansRead the answer and worked solution →Checking an integralRead the answer and worked solution →Tap every true statement about integrationRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →

Worked practice questions

Assertion and reason

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Questions
  1. Reason
    Any two functions with the same derivative differ only by a constant.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    An indefinite integral is written with a trailing constant.
  2. Reason
    The two processes are inverses of each other.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Integration can be checked by differentiating the answer.
  3. Reason
    The integral of a sum is the sum of the integrals.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    The integral of a product is the product of the integrals.
The reason must genuinely explain the assertion. Source: syllabus Maths, Ch 7 Integrals.

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Two are true, one is not

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Questions
  1. False statement
    Indefinite integrals need no constant
    Statements
    1. Integration is the inverse of differentiation
    2. Indefinite integrals carry a constant
    3. Indefinite integrals need no constant
  2. False statement
    Products split under integration
    Statements
    1. Products split under integration
    2. Sums split under integration
    3. Constant factors come outside
  3. False statement
    Every integral of a function is identical
    Statements
    1. All integrals of one function differ by a constant
    2. Every integral of a function is identical
    3. C is the constant of integration
The false line extends a rule that does not extend. Source: syllabus Maths, Ch 7 Integrals.

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Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about indefinite integrals are false.
    Choices
    1. Item
      Sums integrate term by term
      Correct
      Yes
    2. Explanation
      No such rule; that needs integration by parts.
      Item
      Products integrate factor by factor
    3. Explanation
      It is part of the general integral.
      Item
      The constant may be omitted
    4. Explanation
      It is the inverse process.
      Item
      Integration is the same as differentiation
Each trap over-extends a linearity rule. Source: syllabus Maths, Ch 7 Integrals.

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