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

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 31–60 of 121.

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 →Formulae of elementary geometry cannot find areas enclosed by:Read the answer and worked solution →The area under a curve is built from a large number of thin:Read the answer and worked solution →For a vertical strip of height y and width dx, dA equals:Read the answer and worked solution →The area of one thin strip is called the:Read the answer and worked solution →The total area comes from adding up all the:Read the answer and worked solution →The definite integral is evaluated using which theorem?Read the answer and worked solution →Strips used to find an area may be vertical or:Read the answer and worked solution →If a curve lies below the x-axis, its integral comes out:Read the answer and worked solution →When the integral is negative, the area is taken as its:Read 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 →For the region below the axis A1 is negative while A2 is:Read the answer and worked solution →For a horizontal strip, the elementary area would be:Read the answer and worked solution →Areas are found here for lines and arcs of circles, plus:Read the answer and worked solution →The width of an elementary vertical strip is written as:Read the answer and worked solution →The definite integral was first defined as the limit of:Read the answer and worked solution →The height of a vertical elementary strip is given by:Read the answer and worked solution →An elementary area is located at a position specified by some value of:Read the answer and worked solution →Only the numerical value of an area is taken into consideration, so signs are:Read the answer and worked solution →Finding the area of a circle here uses which curves in standard form?Read the answer and worked solution →Match the area termRead the answer and worked solution →True or false about areasRead the answer and worked solution →Order the area methodRead the answer and worked solution →

Worked practice questions

Definite or indefinite?

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Items
  1. Item
    Carries a constant of integration
    Category
    Indefinite integral
  2. Item
    Names a family of functions
    Category
    Indefinite integral
  3. Item
    Has limits attached
    Category
    Definite integral
  4. Item
    Evaluates to a number
    Category
    Definite integral
Categories
  1. Item
    Indefinite integral
  2. Item
    Definite integral
One yields a family, the other a number. Source: syllabus Maths, Ch 7 Integrals.

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Reading the definitions back

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Questions
  1. Question
    Integral calculus asks you to find
    Choices
    1. a derivative from a function
    2. a function from its differential
    3. a limit
    Correct choice
    a function from its differential
  2. Question
    Indefinite integrals are also called
    Choices
    1. definite integrals
    2. partial integrals
    3. general integrals
    Correct choice
    general integrals
  3. Question
    All integrals of a given function differ by
    Choices
    1. a constant
    2. a factor
    3. nothing
    Correct choice
    a constant
Straight recall of the opening. Source: syllabus Maths, Ch 7 Integrals.

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Complete the linearity rules

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Missing parts
  1. Answer
    sum
    Choices
    1. sum
    2. product
    3. difference
  2. Answer
    f(x)
    Choices
    1. f(x)
    2. k
    3. g(x)
Complete the statement
The integral of f(x) + g(x) equals the {0} of their integrals. For any real number k, the integral of k·f(x) equals k times the integral of {1}.
Two rules, both stated in the summary. Source: syllabus Maths, Ch 7 Integrals.

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