HINTS FOR HOMEWORK PROBLEMS FROM CHAPTER 3
Section 3.2
- (1a) See Example 3.2.1.
- (1e) See Example 3.2.2.
- (2a) See Example 3.2.3 (2).
- (2g) See Example 3.2.3 (1).
- (3a) See Example 3.2.4 (2).
- (3g) See Example 3.2.4 (1).
- (4a) See Example 3.2.5 (4).
- (4c) See the right diagram in Figure 14.
- (4g) See Example 3.2.5 (1) and the left diagram in Figure 13.
- (4k) See Example 3.2.5 (2).
- (4n) What is the geometric shape of this region?
- (4p) See Example 3.2.5 (2).
- (5a) This region is the union of a triangle and a trapezoid.
Recall that the area of a trapezoid is its height times half the sum
of the lengths of its bases.
- (6a) You should not need to use calculus here!
- (6c) See Example 3.2.7 (1). The region is a trapezoid.
- (6d) See Example 3.2.7 (1). The region is the union of two trapezoids.
- (7a) See Example 3.2.7 (1). The region is a triangle.
- (7b) See Example 3.2.7 (1). The region is the union of two triangles.
Section 3.3
- (1a) See Example 3.3.1.
- (2a) See Example 3.3.2 (1).
- (2e) See Example 3.3.2 (2).
- (2i) See Example 3.3.2 (4).
- (3b) See Example 3.3.8 (2).
- (3e) See Example 3.3.7 (2).
- (3f) What is the integral of 3/x^2?
- (3j) See Corollary 3.3.5(i).
- (4b) See Example 3.3.3 (1).
- (4g) See Corollary 3.3.5(f).
- (4i) Use the additive property of the definite to
separately calculate the area for x<0 and for x>0.
- (5d) See Example 3.3.4 (2).
- (5f) See Example 3.3.4 (2). Multiply out the function before integrating.
- (6b) See Example 3.3.5 (1).
- (6f) See Example 3.3.5 (2).
- (6i) Note that cos x = sin x when tan x = 1.
- (7a) See Example 3.3.6 (1).
- (7d) Integrate with respect to y, noting x = sin y.
- (7e) Solve for x, and integrate with respect to y.
- (8e) See Corollary 3.3.5(i) and Examples 3.2.7.