Mathematics · JEE | APPLICATION OF INTEGRALS

Consider the following statements regarding the application of definite integrals to find areas: (A) The area bounded by the curve \( y = f(x) \), x-axis, and lines \( x = a, x = b \) is given by \( \int_{a}^{b} y dx \). (B) If the curve lies below the x-axis, the value of the definite integral is negative, but the numerical value of area is taken as absolute value. (C) The area of the region bounded by curve \( x = g(y) \), y-axis, and lines \( y = c, y = d \) is given by \( \int_{c}^{d} x dy \). (D) Integrating with respect to y uses vertical strip elements. Which of the above statements are correct?

1. A
   (A), (B) and (C) only
2. B
   and (D) only
3. C
   (B), (C) and (D) only
4. D
   (A), (B), (C) and (D)