Review practice
Choose a section to work through its questions and solutions. Your progress is shared across pages. Ranges follow collection order; original source labels are kept on each question.
Section 1 · Questions 1–6
Use horizontal rectangles and the complementary region · Recognise a right-endpoint sum and a cube-root limit · +4 more
- Question 1 · Use horizontal rectangles and the complementary region
- Question 2 · Recognise a right-endpoint sum and a cube-root limit
- Question 3 · Match the inner derivative in a radical integral
- Question 4 · Integrate a polynomial times sine twice by parts
- Question 5 · Derive ellipse area, ellipsoid volume and sphere surface area
- Question 6 · Compare an arcsine integral with an absolute-value area
Section 2 · Questions 7–12
Reverse reciprocal-substitution bounds and reuse an integral · Combine inverse-sine integration with two rotation radii · +4 more
- Question 7 · Reverse reciprocal-substitution bounds and reuse an integral
- Question 8 · Combine inverse-sine integration with two rotation radii
- Question 9 · Use horizontal strips for an inverse-sine region
- Question 10 · Split an absolute integral at the sign change
- Question 11 · Transform a square-root exponential volume
- Question 12 · Read a selected region before splitting rotation disks
Section 3 · Questions 13–17
Distinguish a logarithm from its absolute-value graph · Repeat a logarithmic segment with the correct jump values · +3 more
- Question 13 · Distinguish a logarithm from its absolute-value graph
- Question 14 · Repeat a logarithmic segment with the correct jump values
- Question 15 · Use inverse symmetry to integrate only half the lens
- Question 16 · Compare two slice directions and translate an axis of rotation
- Question 17 · Compare work along a curved and straight path