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Indian Navy AA (Artificer Apprentice) Definite Integration — practice questions

Explore 23 free Definite Integration questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Definite Integration questions and exercises with answers

Showing questions 1–23 of 23.

If $f(x)$ is an **even** function, then $\int_{-a}^{a} f(x)\,dx$ equals:Read the answer and worked solution →$\int_0^4 (x - x^2)\,dx$ equals:Read the answer and worked solution →$\int_1^2 \dfrac{\log x}{x^2}\,dx$ 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

If $f(x)$ is an **even** function, then $\int_{-a}^{a} f(x)\,dx$ equals:

  1. $0$
  2. $\int_0^a f(x)\,dx$
  3. $2\int_0^a f(x)\,dx$
  4. $-2\int_0^a f(x)\,dx$
Show answer and solution

Correct answer: C. $2\int_0^a f(x)\,dx$

For even $f$: $f(-x) = f(x)$, so the contributions from $[-a, 0]$ and $[0, a]$ are equal. **Thus $\int_{-a}^{a} f = 2\int_0^a f$.**

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$\int_0^4 (x - x^2)\,dx$ equals:

  1. $-40/3$
  2. $8$
  3. $40/3$
  4. $-8$
Show answer and solution

Correct answer: A. $-40/3$

**Antiderivative:** $x^2/2 - x^3/3$. **Evaluate:** $[x^2/2 - x^3/3]_0^4 = (16/2 - 64/3) - 0 = 8 - 64/3 = (24-64)/3 = -40/3$.

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$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:

  1. $(1 - \log 2)/2$
  2. $\log 2 - 1$
  3. $1 + \log 2$
  4. $\log 2/2$
Show answer and solution

Correct answer: A. $(1 - \log 2)/2$

Integration by parts with $u = \log x$, $dv = dx/x^2$ gives $v = -1/x$: $[-\log x/x]_1^2 + \int_1^2 dx/x^2 = (-\log 2/2 - 0) + [-1/x]_1^2 = -\log 2/2 + (1 - 1/2) = (1 - \log 2)/2$.

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