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AP Intermediate 2nd Year Integrals and Applications — practice questions — page 3

Explore 121 free Integrals and Applications questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integrals and Applications questions and exercises with answers

Showing questions 61–90 of 121.

Vertical or horizontal strip?Read the answer and worked solution →Complete the area ruleRead the answer and worked solution →Pick the right expressionRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Application of integrals bingoRead the answer and worked solution →Definite or indefinite?Read the answer and worked solution →Assertion and reasonRead the answer and worked solution →If part of a curve is above the axis and part below, the areas are:Read the answer and worked solution →Order the area methodRead the answer and worked solution →Order the steps: check an indefinite integralRead the answer and worked solution →Checking an integralRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →By Walli's formula, ∫_0^(π/2) sin^4(x) dx equals:Read the answer and worked solution →Compute ∫ 2x sin(x²) dx using substitution:Read the answer and worked solution →The integral ∫_{-1}^{1} x³ dx equals:Read the answer and worked solution →Complete the linearity rulesRead 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 →Three of these are wrong. Find the one that holds.Read 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 →Reading the definitions backRead the answer and worked solution →True or false: what the constant meansRead the answer and worked solution →Tap every true statement about integrationRead the answer and worked solution →To evaluate $\int x\cos x\, dx$, the best technique is:Read the answer and worked solution →By the Fundamental Theorem of Calculus, ∫_0^2 (3x² + 2x) dx equals:Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →The integral $\int x^3\, dx$ equals:Read the answer and worked solution →

Worked practice questions

Vertical or horizontal strip?

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Left
Vertical
Items
  1. Item
    Area is y dx
    Answer
    Vertical
  2. Item
    Width is dx
    Answer
    Vertical
  3. Item
    Indexed by x
    Answer
    Vertical
  4. Item
    Area is x dy
    Answer
    Horizontal
  5. Item
    Thickness is dy
    Answer
    Horizontal
  6. Item
    Indexed by y
    Answer
    Horizontal
Right
Horizontal
Instructions
Swipe left for vertical, right for horizontal.
_Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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Complete the area rule

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Missing parts
  1. Answer
    dx
    Choices
    1. dx
    2. dy
    3. dA
  2. Answer
    absolute
    Choices
    1. absolute
    2. negative
    3. average
Complete the statement
A vertical strip has area y {0}, and when the integral is negative the area is its {1} value.
Instructions
Drag a word into each gap to finish the sentence.
_Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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Pick the right expression

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Questions
  1. Question
    Area of a vertical elementary strip
    Choices
    1. y dx
    2. x dy
    3. dx dy
    Correct choice
    y dx
  2. Question
    Area of a horizontal elementary strip
    Choices
    1. y dx
    2. x dy
    3. dx dy
    Correct choice
    x dy
  3. Question
    Height of a vertical strip under a curve
    Choices
    1. f of x
    2. f of y
    3. f of A
    Correct choice
    f of x
  4. Question
    What is taken when the integral comes out negative
    Choices
    1. Absolute value
    2. Half the value
    3. Twice value
    Correct choice
    Absolute value
Instructions
Tap the expression that fits the description.
_Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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