Integrating powers and standard functions Problem set B Answers

\(\frac{4}{7}x^{\frac{7}{4}} + c\)

\(-\frac{2}{3}x^{-\frac{3}{2}} + c\)

\(\frac{25}{4}x^{\frac{8}{5}} + c\)

\(\frac{5}{12}x^{\frac{3}{2}} + c\)

\(16x^{\frac{3}{4}} + c\)

1. (a) \(y=9\sin x+c\)
2. (b) \(y=-4\cos x+c\)

\(y=5e^x-3\)

\(y=5\ln x-2\)

\(y=2\sin x+6e^x-3x+c\)

1. (a) \(L=3t^{\frac{2}{3}}+2\)
2. (b) \(L=29\) m

1. (a) \(V=-5e^{-3t}+5\)
2. (b) \(V=4.75\) litres

\(y=9x^{\frac{4}{3}}-6\ln x+\frac{9}{2}x^{\frac{2}{3}}-120\)

\(x+8\sqrt{x}+4\ln|x|+c\)