Course home

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

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 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Question 96

Using the substitution $\sqrt{3x+1}$ , show that

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

may be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are constants to be found.

[4]

Hence find, by algebraic integration, the exact value of

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

giving your answer in simplest form.

[4]

Markscheme

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

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

119 exam-style questions on AQA A Level Maths 1.11.5 Integration by substitution and by parts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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

Question bank

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

Easy Medium Hard

Question 96

Using the substitution $\sqrt{3x+1}$ , show that

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

may be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are constants to be found.

[4]

Hence find, by algebraic integration, the exact value of

\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx

giving your answer in simplest form.

[4]

Markscheme

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

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

119 exam-style questions on AQA A Level Maths 1.11.5 Integration by substitution and by parts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.