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Agniveer Air Force Integral Calculus — practice questions — page 2

Explore 68 free Integral Calculus questions in Agniveer Air Force Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integral Calculus questions and exercises with answers

Showing questions 31–60 of 68.

The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead 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: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead 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 →

Worked practice questions

The Pythagorean identities

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Questions
  1. Question
    cos²x + sin²x equals
    Choices
    1. 0
    2. 1
    3. 2
    Correct choice
    1
  2. Question
    1 + tan²x equals
    Choices
    1. cosec²x
    2. cot²x
    3. sec²x
    Correct choice
    sec²x
  3. Question
    1 + cot²x equals
    Choices
    1. cosec²x
    2. sec²x
    3. tan²x
    Correct choice
    cosec²x
  4. Question
    Which identity involves cosec?
    Choices
    1. 1 + tan²x
    2. 1 + cot²x
    3. cos²x + sin²x
    Correct choice
    1 + cot²x
Straight recall of the three. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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Odd function or even function?

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Items
  1. Item
    sin(−x) = −sin x
    Category
    Odd: f(−x) = −f(x)
  2. Item
    sine
    Category
    Odd: f(−x) = −f(x)
  3. Item
    cos(−x) = cos x
    Category
    Even: f(−x) = f(x)
  4. Item
    cosine
    Category
    Even: f(−x) = f(x)
Categories
  1. Item
    Odd: f(−x) = −f(x)
  2. Item
    Even: f(−x) = f(x)
sin reverses sign with x; cos does not. That single fact settles many sign questions. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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Complete the degree and radian conversion

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Missing parts
  1. Answer
    180
    Choices
    1. 180
    2. 360
    3. 90
  2. Answer
    180
    Choices
    1. 180
    2. 360
    3. 90
Complete the statement
Radian measure equals (π ÷ {0}) times the degree measure. Degree measure equals ({1} ÷ π) times the radian measure.
Both directions, as the summary gives them. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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