Anti-differentiation: reversing the power rule Problem set A Answers

1. (a) \(f(x)=\frac{1}{9}x^{9}+c\)
2. (b) \(f(x)=-\frac{1}{5}x^{-5}+c\)
3. (c) \(f(x)=x+c\)

1. (a) \(y=2x^{7} + c\)
2. (b) \(y=\frac{1}{2}x^{5} + c\)

1. (a) \(y=x^{-4} + c\)
2. (b) \(y=-\frac{1}{8}x^{-6} + c\)

1. (a) \(y=x^{5} - 2x^{3} + 9x + c\)
2. (b) \(y=\frac{1}{4}x^{3} + \frac{5}{6}x^{2} + c\)

\(x^{4} - 5x - 3x^{-2} + c\)

\(-\frac{5}{4}y^{-2} + \frac{1}{3}y^{-4} + c\)

1. (a) \(f(x)=5x^{-2} + c\)
2. (b) \(f(x)=-3x^{-4} + c\)

1. (a) \(f(x)=6x^{3/2} + c\)
2. (b) \(f(x)=20x^{1/2} + c\)

1. (a) \(s=2t^{3} - 5t^{2} + 4t+c\)
2. (b) c = 0

\(S=d^{2} + 6d^{-2}+c\)

\(f(x)=4x^{3/2} - 6x^{1/2} - 4x^{-1}+c\)

Sam differentiated instead of integrating. Correct: \(-2x^{-3}+c\)