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Indian Navy MR Integrals — practice questions

Explore 23 free 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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Integrals questions and exercises with answers

Showing questions 1–23 of 23.

∫ sin³ x dx (using sin³ x = sin x (1 - cos² x)):Read the answer and worked solution →∫₀^(π/2) sin x cos x dx equals:Read the answer and worked solution →$\displaystyle\int e^x\,dx$ 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

∫ sin³ x dx (using sin³ x = sin x (1 - cos² x)):

  1. -cos x + cos³ x/3 + C
  2. cos x - cos³ x/3 + C
  3. sin³ x/3 + C
  4. x sin³ x + C
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Correct answer: A. -cos x + cos³ x/3 + C

sin³ x = sin x (1 - cos² x). Let u = cos x, du = -sin x dx. Integral = -∫ (1 - u²) du = -(u - u³/3) + C = -cos x + cos³ x/3 + C.

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∫₀^(π/2) sin x cos x dx equals:

  1. π/4
  2. 1/2
  3. 0
  4. 1
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Correct answer: B. 1/2

sin x cos x = (1/2) sin(2x). **So integral = (1/2) ∫₀^(π/2) sin(2x) dx = (1/2)[-cos(2x)/2]₀^(π/2) = (1/4)[1 - (-1)] = 1/2.**

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$\displaystyle\int e^x\,dx$ equals:

  1. $e^{x+1} + C$
  2. $e^x + C$
  3. $\dfrac{e^x}{x} + C$
  4. $x e^{x} + C$
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Correct answer: B. $e^x + C$

∫eˣ dx = eˣ + C.

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