Test: Application of Integrals- Assertion & Reason Type Questions - Commerce MCQ

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): If the two curves y = f(x) and y = g(x) intersect at x = a, x = c and x = b, such that a < c="" />< />

If f(x) > g(x) in [a, c] and g(x) £ f(x) in [c, b], then Area of the regions bounded by the curve

= Area of region PACQP + Area of region QDRBQ.

Reason (R): Let the two curves by y = f(x) and y = g(x), as shown in the figure. Suppose these curves intersect at f(x) with width dx.

= Area bounded by the curve {y = f(x)}

–Area bounded by the curve {y = g(x)}, where f(x) > g(x).

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The area enclosed by the circle x² + y² = a² is πa².

Reason (R): The area enclosed by the circle

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The area enclosed by the circle x² + y² = a² is πa².

Reason (R): If the curve under consideration lies below x-axis, then f(x) < 0 from x = a to x = b, the area bounded by the curve y = f(x) and the ordinates x = a, x = b and x-axis is negative. But, if the numerical value of the area is to be taken into consideration, then