Integration (Edexcel IGCSE Further Pure Maths): Exam Questions

Show that

Hence express in the form where and are integers, giving the value of and the value of ,

(i) Find

(ii) Hence evaluate , giving your answer in the form where , and are integers.

Using formulae (opens in a new tab), show that

(i)

(3)

(ii)

(1)

Show that

Hence, or otherwise, solve, giving exact values in terms of

for

use algebraic integration to find the exact value of

Using a formula (opens in a new tab), show that

Using a formula (opens in a new tab), show that

Hence show that

where , and are integers to be found.

Figure 3 shows part of the curve with equation and part of the curve with equation

Point is the intersection of and as shown in Figure 3

Point is the intersection of with the -axis as shown in Figure 3

Point is the intersection of with the -axis as shown in Figure 3

The finite region , shown shaded in Figure 3, is bounded by the -axis, and

Use calculus to find, in its simplest form, the exact area of

Using formulae (opens in a new tab) , show that

(i)

(ii)

Show that

Solve, in radians to 3 significant figures, for , the equation

Using calculus, find the exact value of