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 x^{2} + y^{2} = a^{2} is πa^{2}.
Reason (R): The area enclosed by the circle
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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 x^{2} + y^{2} = a^{2} is πa^{2}.
Reason (R): If the curve under consideration lies below xaxis, 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 xaxis is negative. But, if the numerical value of the area is to be taken into consideration, then
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 of the region bounded by the curve y = x^{2} and the line y = 4 is 3/32.
Reason (R):
Since the given curve represented by the equation y = x^{2} is a parabola symmetrical about yaxis only, therefore, from figure, the required area of the region AOBA is given by
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):
Reason (R): It may happen that some portion of the curve is above xaxis and some portion is below xaxis as shown in the figure. Let A_{1} be the area below the xaxis and A_{2} be the area above the xaxis. Therefore, area bounded by the curve y = f(x), xaxis and the ordinates x = a and x = b is given by Area = A_{1} + A_{2}
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 of region PQML
Reason (R): The area A of the region bounded by curve x = g(y), yaxis and the lines y = c and y = d is given by
204 videos288 docs139 tests

Test: Application of Integrals Case Based Type Questions Test  15 ques 
Important Questions: Applications of Integrals Doc  2 pages 
NCERT Solutions  Exercise Miscellaneous : Application of Integral Doc  1 page 
NCERT Solutions  Exercise 8.1 : Application of Integrals Doc 
NCERT Solutions  Exercise 8.2 : Application of Integrals Doc 
204 videos288 docs139 tests

Test: Application of Integrals Case Based Type Questions Test  15 ques 
Important Questions: Applications of Integrals Doc  2 pages 
NCERT Solutions  Exercise Miscellaneous : Application of Integral Doc  1 page 
NCERT Solutions  Exercise 8.1 : Application of Integrals Doc 
NCERT Solutions  Exercise 8.2 : Application of Integrals Doc 