Answers300P1^
(ii) (^113)
(iii)
(iv) (^113)
(v) The answers are the same,
since the second area is a
translation of the first.
13 (i)
(ii) 24 square units
14 (i)
(ii) 713 square units
(iii) 713 , by symmetry
(iv) (^713)
15 (i)
(ii) (^) ∫^40 (x^2 − 2 x + 1) dx larger,
as area between 3 and 4 is
larger than area between
−1 and 0.
(iii) (^) ∫^3 − 1 (x^2 − 2 x + 1) dx = 513 ;
(^) ∫^40 (x^2 − 2 x + 1) dx = (^913)
16 (i) and (ii)
(iii) (a) 14
(^) (b) 241
(iv) 0.140 625. The maximum
lies before x = 1.5.
17 16 square units
18 (i) 14.4 units
(ii) 8 square units
19 (ii) 7.2 square units
20 (i) y = − (^) x^82 + 12
(ii) x + 2 y = 22
(iii) 8 square units
21 (i) 2 − (^16) x 3 ,^48 x 4
(ii) (2, 6), minimum
(iv) 7 square units
Exercise 6C (Page 196)
1 (i)
2014 squareunits
(ii)
9 square units
(iii)
216 square units
(iv)
1 square units
(v)
4
15 square units
(vi)
(^2161) square units
y
1 2 3
–1
O x
–1O 2 x
y
O 2 3 x
y
1
(^2) x
y
O
–6
2 3 4 x
(D)
(E)
y
x
y
O
–3
y = x^3
x
y
O
y x^2 –4
–2 –1 2
–4
x
y
O
–1
y = x^5 – 2
–2
y
x
1
O
y = 3x^2 – 4x
x
y
–1 O 1
y x^4 –x2
x
y
O
–1
y = 4x^3 – 3x^2
0.75
0.5