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Indian Navy SSR (Sailor) Integrals — practice questions

Explore 21 free Integrals questions in Indian Navy SSR (Sailor) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integrals questions and exercises with answers

Showing questions 1–21 of 21.

The integral ∫ x^n dx (for n ≠ -1) equals:Read the answer and worked solution →Complete the relationship between the two calculiRead the answer and worked solution →True or false: the constant of integrationRead the answer and worked solution →Differentiation or integration?Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →Properties in useRead the answer and worked solution →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

The integral ∫ x^n dx (for n ≠ -1) equals:

  1. $n x^{n-1} + C$ (derivative formula)
  2. $x^{n+1} + C$ (missing divisor)
  3. $x^n + C$ (no change)
  4. $x^{n+1} / (n+1) + C$ (power rule)
Show answer and solution

Correct answer: D. $x^{n+1} / (n+1) + C$ (power rule)

Power rule for integration: ∫x^n dx = x^(n+1)/(n+1) + C, valid for n ≠ -1. For n = -1, ∫(1/x)dx = ln|x| + C.

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Complete the relationship between the two calculi

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Missing parts
  1. Answer
    derivative
    Choices
    1. derivative
    2. integral
    3. limit
  2. Answer
    function
    Choices
    1. function
    2. constant
    3. slope
  3. Answer
    inverse
    Choices
    1. inverse
    2. same
    3. square
Complete the statement
In differential calculus you are given a function and find its {0}. In integral calculus you are given the differential and must find the {1}. So integration is the {2} of differentiation.
Integration undoes differentiation. Source: syllabus Maths, Ch 7 Integrals.

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True or false: the constant of integration

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Questions
  1. Statement is true
    Yes
    Statement
    An indefinite integral carries a constant of integration.
  2. Statement is true
    Yes
    Statement
    All the integrals of one function differ only by a constant.
  3. Statement is true
    No
    Statement
    An indefinite integral names exactly one function.
  4. Statement is true
    Yes
    Statement
    Indefinite integrals are also called general integrals.
  5. Statement is true
    Yes
    Statement
    The constant is usually written C.
Every indefinite integral names a family, not a single function. Source: syllabus Maths, Ch 7 Integrals.

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