Further Integration (A Level only) | Edexcel A Level Maths: Pure Topic Questions 2018

1

2 marks

A student is estimating the area bounded by the curve $y = f (x)$ , the x-axis and the lines $x = a$ and $x = b$ .

The student intends to estimate the area by using trapezia of equal width.

q1-8-2-further-integration-easy-a-level-maths-pure-screenshots

Add to the diagram above to show how the student can use 4 trapezia to estimate the area.

How did you do?

Did this page help you?

1

3 marks

The diagram below shows a sketch of the curve with equation $y = 1 + 2 x - \frac{1}{4} x^{2} .$

q1-8-2-further-integration-hard-a-level-maths-pure-screenshot

The point $P (x, y)$ lies on the curve.

The shaded rectangle shown has width δx and height y.

Calculate

$\lim_{δ x \to 0} \sum_{x = 1}^{8} (1 + 2 x - \frac{1}{4} x^{2}) δ x$

How did you do?

Did this page help you?

This topic pack contains questions on the following:

Integration as the limit of a sum
Integrating Other Functions (Trig, ln & e etc)
Reverse Chain Rule
f'(x)/f(x)
Integration by Substitution (Reverse Chain Rule)
Harder Substitution
Integrating with Trigonometric Identities
Integration by Parts
Integration using Partial Fractions
Area between two curves
Integration Decision Making

1

2 marks

A student is estimating the area bounded by the curve y=fx, the x-axis and the lines $x = a$ and $x = b$ .

The student intends to find the area of two rectangles of equal width in order to estimate the area as shown in the diagram below.

q1-8-2-further-integration-medium-a-level-maths-pure-screenshot

By drawing a sketch, show how the student’s estimate of the area can be improved while still using rectangles of equal width.

How did you do?

Did this page help you?

1

3 marks

The diagram below shows a sketch of the curve with equation $y = 2 e^{0.1 x}$ .

q1-8-2-further-integration-veryhard-a-level-maths-pure-screenshot

A point $P (x, y)$ lies on the curve.

The shaded rectangle shown has width $δ x$ and height $y$ .

Calculate

$\lim_{δ x \to 0} \sum_{x = 2}^{5} 2 e^{0.1 x} δ x$

How did you do?

Did this page help you?

	Download	View
Easy
Medium
Hard
Very Hard

Edexcel A Level Maths: Pure

Topic Questions

8.2 Further Integration (A Level only)

Integration as the limit of a sum

Integrating Other Functions (Trig, ln & e etc)

Reverse Chain Rule

f'(x)/f(x)

Integration by Substitution (Reverse Chain Rule)

Harder Substitution

Integrating with Trigonometric Identities

Integration by Parts

Integration using Partial Fractions

Area between two curves

Integration Decision Making