1.8.8 Integration by substitution (A-level only)

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Question 63

A robotic arm's force output $F$ , in Newtons, is modeled by $x\sqrt{2x-1}$ where $x$ is the extension in metres. Use integration by substitution to show that the total work done $W$ during an extension from $\frac{1}{2}$ to $x = 4$ is given by

\int_{\frac{1}{2}}^{4} x\sqrt{2x-1} \, dx = \frac{91\sqrt{7}}{15}

Fully justify your answer.

[7]

1.8.8 Integration by substitution (A-level only)

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Question 63

A robotic arm's force output $F$ , in Newtons, is modeled by $x\sqrt{2x-1}$ where $x$ is the extension in metres. Use integration by substitution to show that the total work done $W$ during an extension from $\frac{1}{2}$ to $x = 4$ is given by

\int_{\frac{1}{2}}^{4} x\sqrt{2x-1} \, dx = \frac{91\sqrt{7}}{15}

Fully justify your answer.

[7]

1.8.8 Integration by substitution (A-level only)

Question 63

1.8.8 Integration by substitution (A-level only) Questions

1.8.8 Integration by substitution (A-level only)

Question 63

1.8.8 Integration by substitution (A-level only) Questions