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MHT-CET Indefinite Integration — practice questions — page 3

Explore 70 free Indefinite Integration questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Indefinite Integration questions and exercises with answers

Showing questions 61–70 of 70.

If degree of f is at least degree of g, f/g is first rewritten how?Read the answer and worked solution →Splitting into partial fractions, what is the primitive of 1/((x-1)(x-2))?Read the answer and worked solution →Splitting 1/(x(x+1)) into two fractions, what is its antiderivative?Read the answer and worked solution →Let 1/((x-a)(x-b)) = A/(x-a) + B/(x-b). Then A equals what?Read the answer and worked solution →Which is the partial fraction form for 1/((x-1)^2 (x+2))?Read the answer and worked solution →Factorising the quadratic x^2 - 5x + 6, what is the primitive of its reciprocal?Read the answer and worked solution →Dividing first, what is the integral of (x^2 + 1)/(x^2 - 1)?Read the answer and worked solution →For x^2 log x by parts, which function is taken first?Read the answer and worked solution →Which method finds the antiderivative of x cos x most easily?Read the answer and worked solution →Which method suits (3x+1)/((x-1)(x+2)) when integrating?Read the answer and worked solution →

Worked practice questions

If degree of f is at least degree of g, f/g is first rewritten how?

  1. As a product of f and g
  2. As a sum of f and g
  3. As quotient plus remainder/g
  4. As the square of f over g
Show answer and solution

Correct answer: C. As quotient plus remainder/g

Long division expresses an improper fraction as quotient plus a proper remainder fraction.

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Splitting into partial fractions, what is the primitive of 1/((x-1)(x-2))?

  1. log|(x - 1)(x - 2)| + c
  2. log|(x - 2)/(x - 1)| + c
  3. log|(x - 1)/(x - 2)| + c
  4. -1/(x - 1)(x - 2) + c
Show answer and solution

Correct answer: B. log|(x - 2)/(x - 1)| + c

Partial fractions give 1/(x-2) - 1/(x-1), which integrates to log|(x-2)/(x-1)|.

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Splitting 1/(x(x+1)) into two fractions, what is its antiderivative?

  1. log|x(x + 1)| + c
  2. log|x/(x + 1)| + c
  3. -1/(2x + 1) + c
  4. log|(x + 1)/x| + c
Show answer and solution

Correct answer: B. log|x/(x + 1)| + c

Partial fractions give 1/x - 1/(x+1), which integrates to log|x/(x+1)|.

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More Mathematics topics

Permutations and CombinationsProbabilityApplication of DerivativesLinear ProgrammingDifferential EquationsVectorsDefinite IntegrationMatrices