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Application of Integrals

Uttar Pradesh Board · Class 12 · Mathematics

Practice quiz for Application of Integrals — Uttar Pradesh Board Class 12 Mathematics. MCQs and questions with answers to test your preparation.

32 questions20 flashcards5 concepts

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An illustration showing a curve y=f(x) bounded by the x-axis and vertical lines x=a and x=b. The area is approximated by numerous thin vertical rectangular strips, with one representative strip highli
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Quick Quiz: Application of Integrals

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1

Find the area bounded by the curve y = x², the x-axis, and the lines x = 1 and x = 3.

2

The area bounded by y = 4 - x² and the x-axis is:

3

Find the area between the curves y = x² and y = 4x - x².

4

Which method is most appropriate for finding the area bounded by x = y² - 1 and x = 3?

32 Questions·
multiple choicemultiple correcttext answertrue falsematchingorderinglong answer

Sample Questions

1multiple correct

Which of the following integrals correctly represent the area bounded by y = sin x, x-axis, from x = 0 to x = π?

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∫₀^π sin x dx, ∫₀^π |sin x| dx, 2∫₀^(π/2) sin x dx

Since sin x ≥ 0 on [0,π], the area is ∫₀^π sin x dx = 2. The absolute value notation is also correct. Due to symmetry, 2∫₀^(π/2) sin x dx also gives the same result.

2text answer

Calculate the area bounded by y = √x, x-axis, and the line x = 4.

3true false

True or False: The area bounded by y = x³, x-axis, from x = -1 to x = 1 is zero.

Show answer

True

∫₋₁¹ x³ dx = [x⁴/4]₋₁¹ = 1/4 - 1/4 = 0. This is because x³ is an odd function, so the areas above and below the x-axis cancel out over symmetric intervals.

4text answer

The area of the region bounded by x = y² and x = 4 is:

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Frequently Asked Questions

What are the important topics in Application of Integrals for Uttar Pradesh Board Class 12 Mathematics?
Application of Integrals covers several key topics that are frequently asked in Uttar Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Application of Integrals — Uttar Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 32 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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