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Class 12 Application of Integrals worksheet
CBSE Mathematics. Areas under curves: parabolas, lines, circles and ellipses. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The area bounded by y = x², the x-axis and the line x = 3 is:
- 9/2 square units
- 27 square units
- 27/2 square units
- 9 square units
Answer
(d) 9 square units
∫₀³ x² dx = 1 × 27/3
- 2.
The area enclosed by the ellipse x²/81 + y²/64 = 1 is:
- 5184π square units
- 145π square units
- 72π square units
- 18π square units
Answer
(c) 72π square units
πab with a = 9, b = 8
- 3.
The area of the region bounded by the parabola y² = 4x and the line x = 1 is:
- 8 square units
- 16/3 square units
- 4/3 square units
- 8/3 square units
Answer
(d) 8/3 square units
2∫₀¹ 2√x dx = (8/3) × 1 × 1
Section B · short answer
- 4.
Find the area bounded by the curve y = x² + 6x + 15, the x-axis and the lines x = −5 and x = −1.
Answer
88/3 square units
the curve stays above the x-axis; ∫₋₅⁻¹ (x² + 6x + 15) dx
- 5.
Find the area of the region bounded by the parabola y² = 64x and the line x = 16.
Answer
2048/3 square units
2∫₀¹⁶ 8√x dx = (8/3) × 4 × 64
Section C · long answer
- 6.
Using integration, find the area of the triangle with vertices (−2, 0), (4, 1), (5, 6).
Answer
29/2 square units
write the equation of each side, integrate between the vertices' x-values, and add or subtract the areas
Fresh sheets for your child
In the app, every Application of Integrals sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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