Mixed practice: integrals and areas Problem set B Answers

\(\frac{52}{27}\) (1.93)

\(-15\ln5\) (−24.1)

1. (a) \(6\ln3\) (6.59)
2. (b) \(5\ln\frac58\) (−2.35)

\(\ln 5\), which does not contain k

1. (a) a = 4
2. (b) a = 4

1. (a) 34
2. (b) 30

1. (a) \(\ln(3x)+1\)
2. (b) \(2\ln2+\ln3-1\) (1.48)

\(\frac{64-7\sqrt7}{3}\) (15.2)

\(\frac56-\frac13e^{-3}-\frac12e^{-4}\) (0.808)

1. (a) A (0, 1) and B (1.5, 0.0111)
2. (b) 0.295 m²

1. (a) \(\left(\frac\pi4,\frac{\sqrt2}2\right)\)
2. (b) \(2\sqrt2\) (2.83)

1. (a) Both are oscillating curves: g starts at 1 and f at 0; they cross once, at x = 0.681
2. (b) 0.459

Area \(=\frac12+\frac12=1\)

1. (a) \(−4\)
2. (b) \(−3\)
3. (c) 9