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Solutions

Overview

Step-by-step NCERT solutions for Application of Integrals (Chapter 8, CBSE Class 12 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Application of Integrals textbook chapter.

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What these solutions cover

All 9 questions in Application of Integrals are solved in the PDF. Here's what's inside, exercise by exercise:

Exercise 8.1

  1. Find the area of the region bounded by the ellipse x^2/16 + y^2/9 = 1.
  2. Find the area of the region bounded by the ellipse x^2/4 + y^2/9 = 1.
  3. Area lying in the first quadrant and bounded by the circle x^2 + y^2 = 4 and the lines x = 0 and x = 2 is (A) π (B) π/2 (C) π/3 (D) π/4
  4. Area of the region bounded by the curve y^2 = 4x, y-axis and the line y = 3 is (A) 2 (B) 9/4 (C) 9/3 (D) 9/2

Miscellaneous Exercise

  1. Find the area under the given curves and given lines:
    • (i) y = x^2, x = 1, x = 2 and x-axis
    • (ii) y = x^4, x = 1, x = 5 and x-axis
  2. Sketch the graph of y = |x + 3| and evaluate ∫₋₆⁰ |x + 3| dx.
  3. Find the area bounded by the curve y = sin x between x = 0 and x = 2π.
  4. Area bounded by the curve y = x^3, the x-axis and the ordinates x = -2 and x = 1 is (A) -9 (B) -15/4 (C) 15/4 (D) 17/4
  5. The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by (A) 0 (B) 1/3 (C) 2/3 (D) 4/3 [Hint: y = x^2 if x > 0 and y = -x^2 if x < 0]
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More solutions in Mathematics Part II

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More NCERT Solutions for Class 12

Read the Application of Integrals textbook chapter / PDF, or browse all CBSE Class 12 Mathematics solutions.

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