Application of IntegralsClass 12 Mathematics Assertion & Reason Questions

Assertion (A): The area of the region bounded by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is $12\pi$ square units.

Reason (R): The area of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by the formula $\pi ab$.

Assertion (A): The area bounded by the curve $y = \cos x$ between $x=0$ and $x=2\pi$ is 4 square units.

Reason (R): The total area is calculated by $\int_{0}^{2\pi} \cos x \,dx$.

Assertion (A): The area of the region bounded by the curve $y^2 = 4x$, the y-axis and the line $y=3$ is $\frac{9}{2}$ square units.

Reason (R): The area of the region bounded by the curve $x=g(y)$, the y-axis, and the lines $y=c$ and $y=d$ is given by $\int_{c}^{d} x \,dy$.