Applications of Integration (Edexcel IGCSE Further Pure Maths): Exam Questions

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

The curve has equation

The line with equation intersects at two points.

The finite region bounded by the curve and the line is rotated about the -axis.

Use algebraic integration to find, to 3 significant figures, the volume of the solid generated.

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

The curve and the curve intersect at the point

The finite region , shown shaded in Figure 3, bounded by the curve , the curve and the straight line is rotated through 360º about the -axis.

Find, using algebraic integration, the exact volume of the solid formed.

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

The region , bounded by the -axis, the curve and the line , is rotated through 360° about the -axis.

Using algebraic integration, find the exact value of the volume of the solid generated.

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

Given that can be written in the form where , and are constants,

The curve has equation

The curve with equation intersects curve at two points.

Use algebraic integration to find the exact area of the finite region bounded by the curve and the curve

The curve with equation where and the line with equation where intersect at the points and , as shown in Figure 2.

The finite region bounded by and , shown shaded in Figure 2, is rotated through radians about the -axis.

Use algebraic integration to find the volume of the solid generated.
Give your answer in terms of

Expand in ascending powers of up to and including the term in

Where appropriate express each coefficient as an exact fraction in its lowest terms.

Hence, using algebraic integration, obtain an estimate of

Give your answer to 5 significant figures.

Figure 2 shows the graph of part of the curve with equation
The finite region enclosed by the curve and the straight line with equation is rotated through 360° about the -axis.

Use algebraic integration to find the exact volume of the solid generated.
Give your answer in terms of

where and are prime numbers

Given that the fourth and fifth terms, in ascending powers of , in the series expansion of are 20and 48 respectively,

Using the first five terms, in ascending powers of , in the series expansion of

obtain an estimate, to 4 significant figures, of

The region , shown shaded in Figure 2, is bounded by the curve with equation and the curve with equation

The two curves intersect at the point and at the point .

The region is rotated through 360° about the ‑axis.

Use algebraic integration to find the volume, to 2 decimal places, of the solid generated.

Figure 3 shows part of the curve with equation
The curve crosses the -axis at the point and the -axis at the point .

The finite region is bounded by , and the -axis.

Using calculus, find the area of .
Give your answer to one decimal place.