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Important Questions

Application of Integrals — Important Questions

Madhya Pradesh Board · Class 12 · Mathematics

98 important questions from Application of Integrals for Madhya Pradesh Board Class 12 Mathematics, with answers. Written for the board exams 2027.

98 questions60 flashcards16 formulas & key relations5 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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98 Questions·
multiple choicetext answertrue falsematchingorderingmultiple correctlong answernumerical

Important Questions from Application of Integrals

1text answer

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

2true 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.

3text answer

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

4matching

Match the following curves with their areas from x = 0 to x = 2:

Show answer

y = x → Area = 2

∫₀² x dx = [x²/2]₀² = 2; ∫₀² x² dx = [x³/3]₀² = 8/3; ∫₀² 2x dx = [x²]₀² = 4; ∫₀² 1 dx = [x]₀² = 2

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Frequently Asked Questions

What are the important topics in Application of Integrals for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Application of Integrals include Core Idea of Area by Integration, Negative Area and Mixed Area, Standard Results for Circle and Ellipse, Worked Examples to Remember. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How many important questions are there in Application of Integrals?
Super Tutor has 98 practice questions for Application of Integrals, including multiple choice, text answer, true false, matching, ordering, multiple correct, long answer, numerical questions. A sample with answers is on this page.

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

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All Madhya Pradesh Board Class 12 Mathematics Important Questions

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