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CUET UG Integrals and Applications — practice questions — page 2

Explore 38 free Integrals and Applications questions in CUET UG 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 31–38 of 38.

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 →If a curve lies below the x-axis, its integral comes out:Read the answer and worked solution →For the region below the axis A1 is negative while A2 is: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 →Formulae of elementary geometry cannot find areas enclosed by:Read the answer and worked solution →

Worked practice questions

The definite integral is evaluated using which theorem?

  1. Pythagoras Theorem
  2. Fundamental Theorem
  3. Remainder Theorem
  4. Binomial Theorem
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Correct answer: B. Fundamental Theorem

1. Definite integrals were first defined as the limit of a sum. 2. A theorem lets them be evaluated from antiderivatives instead. 3. That is the Fundamental Theorem of Calculus. 4. So the answer is Fundamental Theorem. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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Areas are found here for lines and arcs of circles, plus:

  1. Parabolas and ellipses
  2. Cubes and cylinders
  3. Spheres and prisms
  4. Cones and pyramids
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Correct answer: A. Parabolas and ellipses

1. Only standard curves are handled here. 2. Circles are one of them. 3. Parabolas and ellipses complete the list. 4. So the answer is parabolas and ellipses. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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The definite integral was first defined as the limit of:

  1. A root
  2. A pair
  3. A sum
  4. A ratio
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Correct answer: C. A sum

1. Strips are added up and then made ever thinner. 2. The result is a limiting process on that total. 3. So the definite integral is the limit of a sum. 4. The answer is sum. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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