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Mathematics · JEE | APPLICATION OF INTEGRALS
हिन्दीConsider the following statements regarding the symmetry and areas of standard curves: (A) The circle \( x^2 + y^2 = a^2 \) is symmetrical about both x-axis and y-axis. (B) The total area enclosed by the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) is \( \pi ab \). (C) The curve \( y = \cos x \) from \( x = 0 \) to \( x = 2\pi \) has total bounded area equal to 2. (D) For regions crossing the x-axis, total area is calculated by summing the absolute values of integrals over sub-intervals. How many of the above statements are correct?
View Answer & Solution
Correct answer · Option B
Only three
Explanation
Statements (A), (B), and (D) are correct. Statement (C) is incorrect because the area of \( y = \cos x \) from \( 0 \) to \( 2\pi \) evaluates to \( 1 + 2 + 1 = 4 \). Thus only three statements are correct.
