The “Application of Integrals” chapter connects integral calculus with real geometric quantities—areas, volumes of solids of revolution, and centroids. It frequently appears in board exams (as integration-by-area/volume problems) and competitive exams (as multi-step integral + geometry reasoning), so mastering setup, limits, and correct formula selection is essential for scoring well.
20
Minutes
15
Questions
1 / -0
Marking
Q1. (Find the area of the region enclosed between the parabola and the line .)
Q2. (Find the area of the region enclosed between the curves and .)
Q3. (Find the area of the region enclosed by the curves and .)
Q4. (Assertion (A): The area of the region bounded by the curve for and the -axis is zero.
Reason (R): and converges, so the region has finite area.)
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 and R is false.
A is false and R is true.
Q5. (Compute the area of the region enclosed between the curves and on the interval .)
Q6. Find the area enclosed between and .
Q7. The region bounded by and is rotated about the vertical line . The volume of the solid generated is
Q8. Let be the region in the first quadrant bounded by and . Find the -coordinate of the centroid of .
Q9. The region bounded by and for is revolved about the line . The volume of the resulting solid equals
Q10. Let be the region bounded by the parabola and the line (with ). The -coordinate of the centroid of is
Q11. Find the area of the region enclosed by the curves and .
Q12. The plane region bounded by and (for ) is considered. The -coordinate of its centroid is
Q13. The region bounded by and for is revolved about the line . The volume of the solid generated is
Q14. Let be the area enclosed between and . For which real values of does the area enclosed between and equal ?
Q15. The region bounded by and for is revolved about the vertical line . The volume of the resulting solid is