Application of Integrals
Madhya Pradesh Board · Class 12 · Mathematics
Most important questions from Application of Integrals for Madhya Pradesh Board Class 12 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Calculate the area bounded by y = √x, x-axis, and the line x = 4.
True or False: The area bounded by y = x³, x-axis, from x = -1 to x = 1 is zero.
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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.
The area of the region bounded by x = y² and x = 4 is:
Match the following curves with their areas from x = 0 to x = 2:
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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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