Course home

1.8 Integration

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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

Question 112

The cross-section of a precision-engineered lens is modeled by a curve $y = f (x)$ , for $x > 0$ . The rate of change of the gradient of the profile is given by

\frac{15}{4\sqrt{x^7}} - 6x

A point $P (1, 1.5)$ lies on the boundary of the lens profile.

Given that the gradient of the curve $f^{'} (x) = 0.75$ at point $P$ ,

find the equation of the normal at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are constants,

[3]

find $f (x)$ .

[5]

Markscheme

1.8 Integration Questions

A Level
Maths
1.8 Integration

160 exam-style questions on WJEC A Level Maths 1.8 Integration, covering 1.8.1 Integration, 1.8.2 Integration, and 1.8.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

1.8 Integration

Question bank

1.8 Integration

Easy Medium Hard

Question 112

The cross-section of a precision-engineered lens is modeled by a curve $y = f (x)$ , for $x > 0$ . The rate of change of the gradient of the profile is given by

\frac{15}{4\sqrt{x^7}} - 6x

A point $P (1, 1.5)$ lies on the boundary of the lens profile.

Given that the gradient of the curve $f^{'} (x) = 0.75$ at point $P$ ,

find the equation of the normal at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are constants,

[3]

find $f (x)$ .

[5]

Markscheme

1.8 Integration Questions

A Level
Maths
1.8 Integration