The chapter “Application of Integrals” is crucial because it builds the core integral techniques used across Class 12 board exams and competitive tests—especially for finding areas, volumes of solids of revolution, and centroids. Mastery here strengthens your ability to set correct bounds, choose the right method (washers/shells), and perform integration accurately—skills directly tested in JEE/NEET-style math problems.
20
Minutes
15
Questions
1 / -0
Marking
Q1. Let be the region enclosed by the curves and . What is the area of ?
Q2. Find the positive value of such that the area enclosed between the curves and is square units.
Q3. The region bounded by , and is revolved about the -axis. What is the volume of the solid formed?
Q4. Assertion (A): The area enclosed by the curve and the -axis between and is .
Reason (R): because the integrand is an odd function.
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 false but R is true.
Both A and R are false.
Q5. Let be the region bounded by , the -axis and the vertical line , for . When is revolved, which statement is correct?
Revolution about both axes gives finite volumes, each equal to .
Revolution about the -axis gives finite volume , while revolution about the -axis gives infinite volume.
Revolution about the -axis gives infinite volume, while revolution about the -axis gives finite volume .
Revolutions about both axes give infinite volumes.
Q6. Find the area of the region enclosed by the curves and .
Q7. For the region bounded by and , find the x-coordinate of the centroid of the region.
Q8. Compute the area of the region bounded by the parabola and the line .
Q9. A lamina occupies the region bounded by and (between their intersection points). The density at any point is proportional to its distance from the y‑axis, i.e. . Find the x‑coordinate of the centroid of this lamina.
Q10. The curve meets the x‑axis at . Find the area of the region bounded by the curve and the x‑axis between and .
Q11. Find the area of the region enclosed by the curves and .
Q12. The curves and enclose a region in the first quadrant. Its area is
Q13. The region bounded by , the -axis and the vertical lines and is revolved about the -axis. The volume of the solid of revolution is
Q14. Let be the region bounded by and for . The solid obtained by revolving about the line has volume equal to
Q15. Consider the curve and its horizontal asymptote . The area of the region between the curve and the line from to is