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ISC Class 12 Integrals and Applications — practice questions — page 3

Explore 97 free Integrals and Applications questions in ISC Class 12 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 97.

When the integral is negative, the area is taken as its:Read the answer and worked solution →The area of one thin strip is called the:Read the answer and worked solution →Strips used to find an area may be vertical or: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 →The width of an elementary vertical strip is written as:Read the answer and worked solution →Application of integrals bingoRead the answer and worked solution →Pick the right expressionRead the answer and worked solution →Vertical or horizontal strip?Read the answer and worked solution →Complete the area ruleRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →For a horizontal strip, the elementary area would be: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 →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 →$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{\sqrt{1 - x^2}}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \sec^2 x\,dx$ equals:Read the answer and worked solution →The definite integral is evaluated using which theorem?Read the answer and worked solution →Areas are found here for lines and arcs of circles, plus:Read the answer and worked solution →The definite integral was first defined as the limit of:Read the answer and worked solution →The total area comes from adding up all the:Read the answer and worked solution →Match the area termRead the answer and worked solution →If a curve lies below the x-axis, its integral comes out:Read the answer and worked solution →$\displaystyle\int \log x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:Read the answer and worked solution →Using the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:Read the answer and worked solution →Properties in useRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Which process is being described?Read the answer and worked solution →

Worked practice questions

When the integral is negative, the area is taken as its:

  1. Absolute value
  2. Negative value
  3. Doubled amount
  4. Halved measure
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Correct answer: A. Absolute value

1. Area is a physical size and cannot be negative. 2. Only the numerical value matters. 3. So the absolute value of the integral is taken. 4. The answer is absolute value. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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The area of one thin strip is called the:

  1. Fundamental area
  2. Complete section
  3. Absolute portion
  4. Elementary area
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Correct answer: D. Elementary area

1. Each strip contributes a small piece of the total. 2. That piece sits at some position between a and b. 3. It is called the elementary area. 4. So the answer is elementary area. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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Strips used to find an area may be vertical or:

  1. Circular
  2. Spherical
  3. Horizontal
  4. Triangular
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Correct answer: C. Horizontal

1. A region can be sliced in more than one direction. 2. Sometimes slicing the other way is simpler. 3. So strips may be horizontal instead of vertical. 4. The answer is horizontal. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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