1.11.5 Integration by substitution and by parts (A-level only)

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Question 69

Determine $dθ\int \frac{\sin 2\theta}{1 + \sin \theta} \, d\theta$

[4]

ii.

A research team monitors the rate of energy consumption, $E$ (in gigajoules per hour), of a large-scale data center. The rate is modeled by the function $\frac{18t}{\sqrt{2t + 3}}$ , where $t$ is the time in hours since midnight.

Use the substitution $\sqrt{2t + 3}$ to show that

\int \frac{18t}{\sqrt{2t + 3}} \, dt = 2(2t + 3)^{\frac{1}{2}}(At + B) + k

where $A$ and $B$ are integers to be found and $k$ is an arbitrary constant.

[6]

Determine $dθ\int \frac{\sin 2\theta}{1 + \sin \theta} \, d\theta$

[4]

Use the substitution $\sqrt{2t + 3}$ to show that

\int \frac{18t}{\sqrt{2t + 3}} \, dt = 2(2t + 3)^{\frac{1}{2}}(At + B) + k

where $A$ and $B$ are integers to be found and $k$ is an arbitrary constant.

1.11.5 Integration by substitution and by parts (A-level only)

Question 69

Markscheme

1.11.5 Integration by substitution and by parts (A-level only)

Question 69

Markscheme

1.11.5 Integration by substitution and by parts (A-level only)

Question 69

1.11.5 Integration by substitution and by parts (A-level only) Questions

1.11.5 Integration by substitution and by parts (A-level only)

Question 69

1.11.5 Integration by substitution and by parts (A-level only) Questions