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Application of Integrals — NEET Maths MCQs

30 questions written by hand against the NCERT chapter. Every wrong option is explained, not just the right one.

30questions
10/14/6easy / medium / hard
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Sample questions from this chapter

Area under y=x from x=0 to x=2 is
  1. 2 ✓
  2. 4
  3. 1
  4. 0
Answer: A. The region is a triangle, not a 2-by-2 rectangle. Equivalently, ∫₀²x dx=[x²/2]₀²=2.
Why not B: Uses the endpoint height times full width as a rectangle.
Why not C: Uses only half the triangle base-height product incorrectly.
Why not D: Subtracts equal endpoint function values.
Area under y=sin x from x=0 to π is
  1. 0
  2. 1
  3. 2 ✓
  4. π
Answer: C. The sine curve is nonnegative on [0,π], so its signed integral is its area. Using the antiderivative −cos x gives [−cos x]₀^π=1−(−1)=2; equal endpoint sine values do not make the area zero.
Why not A: Uses endpoint sine values.
Why not B: Keeps only half an arch.
Why not D: Replaces sin x by 1.
Area under y=eˣ above the x-axis from x=0 to ln2 is
  1. 1 ✓
  2. 2
  3. ln2
  4. 1/2
Answer: A. Because eˣ is its own antiderivative, evaluate both bounds: [eˣ]₀^ln2=e^ln2−e⁰=2−1=1. Reporting 2 would omit the lower-limit value.
Why not B: Uses only the upper antiderivative value.
Why not C: Treats the curve as constant height 1.
Why not D: Halves the correct difference.

These are 3 of the 30 questions in the test. Take the full chapter test →

Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Application of Integrals →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsLinear InequalitiesPermutations and Combinations

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Questions

How many NEET questions are there on Application of Integrals?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 12 chapter.

Is this NEET Maths chapter test free?

Yes. Every chapter test is free with no login, and you get your all-India rank on every one. Nothing on the site is on sale right now.

Do the questions explain the wrong options?

Yes — every distractor carries its own explanation naming the specific misconception that makes a student pick it. That is the part most question banks skip, and it is the part that changes your next attempt.