The chapter “Application of Integrals” is crucial for Class 12 board and competitive exams because it links integral calculus with real geometric quantities—areas, volumes of solids of revolution, centroid and moments, and related convergence/divergence results. Mastering standard integral setups (limits, washers/shells) and interpreting results (finite/infinite) helps score reliably in both theory and numerical problems.
25
Minutes
20
Questions
1 / -0
Marking
Q1. Find the area of the region enclosed by the curves and .
Q2. The region is bounded by the parabola and the line . The area of is
Q3. The region bounded by and for is revolved about the line . The volume of the solid of revolution is
Q4. Let be continuous and invertible on with and . Consider the statements:
Statement A:
Statement R: The identity follows by the substitution in the second integral giving .
Both A and R are true but R is not a correct explanation of A.
Both A and R are false.
A is true but R is false.
Both A and R are true and R is a correct explanation of A.
Q5. Find the area of the region enclosed by the parabola and the line .
Q6. Find the area of the region bounded by the curve and the -axis.
Q7. The region enclosed by the curves and in the first quadrant has area equal to
Q8. Let be the region in the first quadrant bounded by and for . If is the volume obtained by revolving about the -axis and the volume obtained by revolving about the -axis, then
Q9. For the region under the curve for (above the -axis), the -coordinate of the centroid is
Q10. Assertion (A): The area under the curve over is infinite. Reason (R): The volume generated by revolving the same region about the -axis is finite.
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true but (R) is not the correct explanation of (A).
(A) is true but (R) is false.
(A) is false but (R) is true.
Q11. Find the area of the region enclosed by the curves and .
Q12. The region bounded by the curves and is revolved about the -axis. The volume of the solid generated is
Q13. The area of the region enclosed by the parabola and the line is
Q14. Assertion (A): For a smooth positive function on , the surface area of the solid generated by revolving the curve about the -axis is given by
Reason (R): For any constant , the surface area of the solid generated by revolving about the -axis equals times the surface area generated by .
Both A and R are true and R is a correct explanation of A
A is true, R is false
Both A and R are true but R is not a correct explanation for A
A is false, R is true
Q15. For which values of does the solid obtained by revolving the region bounded by , the -axis and the vertical line (for ) about the -axis have finite volume but infinite surface area?
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...and 5 more challenging questions available in the interactive simulator.