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Indian Navy Pilot Integral Calculus — practice questions

Explore 25 free Integral Calculus questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integral Calculus questions and exercises with answers

Showing questions 1–25 of 25.

Fundamental theorem of calculus: ∫ from a to b f'(x) dx =Read the answer and worked solution →∫ x ln x dx (integration by parts: u = ln x, dv = x dx):Read the answer and worked solution →The probability of getting an even number on a single throw of a die is: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 →Tap what is true of integrationRead the answer and worked solution →Indefinite or definite?Read the answer and worked solution →

Worked practice questions

Fundamental theorem of calculus: ∫ from a to b f'(x) dx =

  1. f(b) × f(a)
  2. f(b) + f(a)
  3. f(b) - f(a)
  4. 0
Show answer and solution

Correct answer: C. f(b) - f(a)

**FTC Part 2:** ∫_a^b f'(x) dx = f(b) - f(a). Connects integration and differentiation as inverse operations.

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∫ x ln x dx (integration by parts: u = ln x, dv = x dx):

  1. x ln x
  2. (ln x)²
  3. x² ln x - x²/2
  4. (x²/2) ln x - x²/4 + C
Show answer and solution

Correct answer: D. (x²/2) ln x - x²/4 + C

u = ln x, du = dx/x; dv = x dx, v = x²/2. ∫ x ln x dx = (x²/2) ln x - ∫ (x²/2)(1/x) dx = (x²/2) ln x - x²/4 + C.

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The probability of getting an even number on a single throw of a die is:

  1. $\tfrac23$
  2. $\tfrac12$
  3. $\tfrac16$
  4. $\tfrac13$
Show answer and solution

Correct answer: B. $\tfrac12$

Even numbers on a die are {2,4,6}: 3 of 6 outcomes ⟹ 3/6 = 1/2.

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