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CBSE Class 12 (Commerce) Integrals — practice questions — page 2

Explore 102 free Integrals questions in CBSE Class 12 (Commerce) 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 31–60 of 102.

Any two antiderivatives of one function differ only by a:Read the answer and worked solution →The arbitrary C added to every indefinite integral is named:Read the answer and worked solution →Differentiating which expression produces 3x^2?Read the answer and worked solution →A student integrates cos x. What should she write?Read the answer and worked solution →Which result is right for the antiderivative of sin x?Read the answer and worked solution →Find the function whose derivative is sec x tan x.Read the answer and worked solution →What is obtained on integrating cosec x cot x?Read the answer and worked solution →For x not zero, the antiderivative of 1/x is:Read the answer and worked solution →Which expression equals the integral of tan x?Read the answer and worked solution →The result of integrating sec x is:Read the answer and worked solution →Pulling a constant k out: the integral of k f(x) dx equals:Read the answer and worked solution →Integrate 4x^3 - 6x term by term.Read the answer and worked solution →What is the integral of sqrt(x) over x > 0?Read the answer and worked solution →Antidifferentiate 1/x^2 for x not zero.Read the answer and worked solution →Work out the integral of e^(2x).Read the answer and worked solution →If t = 3x is substituted, the integral of cos 3x becomes:Read the answer and worked solution →Use t = x^2 on 2x e^(x^2) dx; the antiderivative is:Read the answer and worked solution →Since 2x is the derivative of 1 + x^2, the integral of 2x/(1 + x^2) is:Read the answer and worked solution →Put t = 1 + x^3 and find the integral of x^2 / (1 + x^3).Read the answer and worked solution →Which is the antiderivative of (2x + 1)^3?Read the answer and worked solution →Substituting t = 1 + cos x, the integral of sin x/(1 + cos x) is:Read the answer and worked solution →Using tan^2 x = sec^2 x - 1, integrate tan^2 x:Read the answer and worked solution →Using the half-angle identity, cos^2 x integrates to:Read the answer and worked solution →Integrating sin^2 x via (1 - cos 2x)/2 gives:Read the answer and worked solution →Put t = sin x: the integral of cos x / sin^2 x is:Read the answer and worked solution →Expand (x + 1/x)^2 and integrate to get:Read the answer and worked solution →1/(1 + x^2) is the derivative of which function?Read the answer and worked solution →Name the antiderivative of 1/sqrt(1 - x^2).Read the answer and worked solution →Given the form 1/(x^2 + a^2), integrate 1/(x^2 + 9).Read the answer and worked solution →Evaluate: integral of dx / sqrt(4 - x^2).Read the answer and worked solution →

Worked practice questions

Any two antiderivatives of one function differ only by a:

  1. Variable term
  2. Reciprocal term
  3. Linear factor
  4. Constant term
Show answer and solution

Correct answer: D. Constant term

If F and G both have derivative f, then F minus G has zero derivative and so is constant.

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The arbitrary C added to every indefinite integral is named:

  1. Order of integration
  2. Path of integration
  3. Index of integration
  4. Constant of integration
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Correct answer: D. Constant of integration

C is the arbitrary constant added because every antiderivative can shift by a constant.

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Differentiating which expression produces 3x^2?

  1. 3x^3
  2. 6x
  3. x^2/3
  4. x^3
Show answer and solution

Correct answer: D. x^3

Raising the power to 3 and dividing by 3 gives x^3, whose derivative is 3x^2.

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More Mathematics topics

Vector AlgebraDeterminantsApplication of IntegralsLinear ProgrammingRelations and FunctionsContinuity and DifferentiabilityApplication of DerivativesThree Dimensional Geometry