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Indian Navy 10+2 B.Tech Cadet Definite Integration — practice questions

Explore 24 free Definite Integration questions in Indian Navy 10+2 B.Tech Cadet 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 1–24 of 24.

For a definite integral with limits swapped, which identity holds?Read the answer and worked solution →$\int_1^3 x\,dx$ equals:Read the answer and worked solution →If $f(x) = x^3 \sin^4 x$, then $\int_{-\pi/4}^{\pi/4} f(x)\,dx$ equals:Read the answer and worked solution →Evaluate $\int_2^3 7^x\,dx$: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

For a definite integral with limits swapped, which identity holds?

  1. $\int_a^b f\,dx = \int_b^a f\,dx$
  2. $\int_a^b f\,dx = -\int_b^a f\,dx$
  3. $\int_a^b f\,dx = \int_b^a f\,dx + c$
  4. $\int_a^b f\,dx = 1/\int_b^a f\,dx$
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Correct answer: B. $\int_a^b f\,dx = -\int_b^a f\,dx$

**Property II:** swapping limits flips the sign. $\int_a^b f\,dx = g(b)-g(a) = -[g(a)-g(b)] = -\int_b^a f\,dx$.

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$\int_1^3 x\,dx$ equals:

  1. 2
  2. 4
  3. 5
  4. 9
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Correct answer: B. 4

$\int_1^3 x\,dx = [x^2/2]_1^3 = 9/2 - 1/2 = 8/2 = 4$.

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If $f(x) = x^3 \sin^4 x$, then $\int_{-\pi/4}^{\pi/4} f(x)\,dx$ equals:

  1. $0$
  2. $\pi/4$
  3. $1$
  4. $2\int_0^{\pi/4} f\,dx$
Show answer and solution

Correct answer: A. $0$

$f(-x) = (-x)^3 \sin^4(-x) = -x^3 \cdot \sin^4 x = -f(x)$. So $f$ is **odd**, and over the symmetric interval the integral is 0.

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