Course home

11.5 Integration by Substitution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Question 26

Using the substitution $\frac{3}{2}\sin 2x$ , show that

\int_0^{\frac{\pi}{2}} e^{3x + \frac{3}{2}\sin 2x} \cos^2 x \, dx = \frac{1}{6}(e^{\frac{3\pi}{2}} - 1)

[4]

The design of a high-performance aerodynamic component involves a surface generated by rotating a region $R$ through $2π2\pi$ radians about the $x$ -axis. The region $R$ is bounded by the curve with equation

\sqrt{18} e^{\frac{3}{2}x + \frac{3}{4}\sin 2x} \cos x

and the coordinate axes in the first quadrant.

Use the result from part (a) to find the volume of the component, giving your answer in simplest form.

[3]

Markscheme

11.5 Integration by Substitution Questions

A Level
Maths
11.5 Integration by Substitution

59 exam-style questions on Edexcel A Level Maths 11.5 Integration by Substitution. Each one has a worked solution and a mark scheme showing where the marks go.

11.5 Integration by Substitution

Question bank

11.5 Integration by Substitution

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Question 26

Using the substitution $\frac{3}{2}\sin 2x$ , show that

\int_0^{\frac{\pi}{2}} e^{3x + \frac{3}{2}\sin 2x} \cos^2 x \, dx = \frac{1}{6}(e^{\frac{3\pi}{2}} - 1)

[4]

\sqrt{18} e^{\frac{3}{2}x + \frac{3}{4}\sin 2x} \cos x

and the coordinate axes in the first quadrant.

Use the result from part (a) to find the volume of the component, giving your answer in simplest form.

[3]

Markscheme

11.5 Integration by Substitution Questions

A Level
Maths
11.5 Integration by Substitution

59 exam-style questions on Edexcel A Level Maths 11.5 Integration by Substitution. Each one has a worked solution and a mark scheme showing where the marks go.