Mixed practice: integrals and areas Problem set A Answers

\(\frac{48}{25}\) (1.92)

\(-16\ln 2\) (−11.1)

1. (a) \(4\ln2\) (2.77)
2. (b) \(-\ln2\) (−0.693)

\(\ln 3\), which does not contain k

1. (a) a = 3
2. (b) a = 3

1. (a) 24
2. (b) 27

1. (a) \(\ln(2x)+1\)
2. (b) \(2\ln2+3\ln3-2\) (2.68)

\(9-\frac{5\sqrt5}{3}\) (5.27)

\(\frac32-e^{-1}-\frac12e^{-2}\) (1.06)

1. (a) A (0, 1) and B (2, 0.0183)
2. (b) 0.391 m²

1. (a) \(\left(\frac\pi4,\frac{\sqrt2}2\right)\)
2. (b) \(2\sqrt2-2\) (0.828)

1. (a) Both are oscillating curves: g starts at 1 and f at 0; they cross once, at x = 0.886
2. (b) 0.611

Area \(=\frac23+\frac23=\frac43\)

1. (a) \(−2\)
2. (b) \(−1\)
3. (c) 8