# Form 4 Mathematics area and approximation: Integration questions and answers

Form 4 Mathematics area and approximation: Integration questions and answers

Lessons (**10**) * SHARE*

- 1.
(a) The gradient of the curve #y=ax^2 + bx# at the origin is equal to 8. Find the values of a and b if the curve has a maximum point at x=4. (b) Determine the area of the region bounded by the lines x=0, x=6, y=0 and the curve #y=x^2 + bx#, for the values of a and b obtained in part (a).

5m 49s - 2.
Determine the area bounded by the curve #y=x^2 - 4#, the x-axis and the line x=4.

3m 5s - 3.
Find the area enclosed by the curve #y=4x-x^2#, the x-axis and the lines x=1 and x=2.

2m 4s - 4.
Find the area bounded by the curve #y=2x^3-5#, the x-axis and the lines x=2 and x=4.

2m 4s - 5.
(a) Find the values of x at which the curve #y=x^2-2x-3# crosses the x-axis. (b) Find #int(x^2-2x-3)dx# (c) Find the area bounded by the curve #y=x^2-2x-3#, the x-axis and the lines x=2 and x=4.

5m 46s - 6.
The curve of the equation #y=2x + 3x^2#, has #x=-2/3# and x=0 as x-intercepts. The area bounded by the curve, x-axis, #x=-2/3# and x=2 is shown by the sketch below. Find: (a) #int(2x+3x^2)dx#. (b) The area bounded by the curve, x-axis, #x=-2/3# and x=2.

4m 54s - 7.
The gradient function of a curve is given by the expression 2x+1. If the curve passes through the point (-4, 6); (a) Find: (i) The equation of the curve (ii) The values of x at which the curve cuts the x-axis. (b) Determine the area enclosed by the curve and the x-axis.

8m 49s - 8.
(a) Complete the table below for the function #y=x^2-3x+6# in the range #2le x le8#
(b) Use the trapezium rule with 10 strips to estimate the area bounded by the curve, #y=x^2-3x+6#, the lines x=-2, x=8, and the x-axis.
(c) Use the mid-ordinate rule with 5 strips to estimate the area bounded by the curve, #y=x^2-3x+6#, the lines x=-2, x=8, and the x-axis.
(d) By integration, determine the actual

9m 47s - 9.
Evaluate #int _2^4 x^2 + 2x - 15\ dx#

1m 41s - 10.
Find the value of k if #int_0^2(kx^3 – 3x^2)dx=16#

1m 41s

### Related Content

- Form 4 Mathematics Trigonometry III Online Lessons
In this session, we are going to learn about trigonometry III, which is a form 4 mathematics topic.

7 Video Lessons

- Form 4 Chemistry Online Lessons on Extraction of Iron
Form 4 Chemistry Online Lessons on Extraction of Iron. All lessons are in video format and pdf.

4 Video Lessons

- Form 4 Physics Floating and Sinking Questions and Answers
In this session, we are going to solve floating and sinking questions for Physics Form 4.

24 Video Lessons

- Form 4 Mathematics area and approximation:Trapezoidal rule questions and answers
In this online session, we are going to answer Form 4 Mathematics area and approximation:Trapezoidal rule questions. Answers are in video format.

10 Video Lessons

- Area and Approximation: Counting squares techniques questions and answers
Form 4 Mathematics Area and Approximation: Counting squares techniques questions and answers

2 Video Lessons

- Form 4 Biology: Evolution Lessons
Form 4 Biology Evolution Lessons. In this session, we are going to learn about evolution. Evolution is a form 4 Biology topic.

6 Video Lessons

- Form 4 Physics X-Rays Questions and Answers
In this session, we are going to solve form 4 Physics X-Rays questions. Answers are available in video format. The questions are suitable for those preparing for KCSE exams.

16 Video Lessons

- Form 4 Biology Genetics Questions and Answers
In this session, we are going to solve several Form 4 Biology questions on genetics. All questions are exam quality and very suitable for those preparing for KCSE exam.

33 Video Lessons

- Kiswahili Fasihi Simulizi Lessons and Notes
Kiswahili Fasihi Simulizi Lessons and Notes. In this session, we are going to learn about fasihi simulizi. Lessons are available in video format. For each lesson, notes in pdf version are also available.

162 Video Lessons

- Form 4 Mathematics : Longitudes and Latitudes Topical Questions and Answers
Form 4 Mathematics : Longitudes and Latitudes Topical Questions and Answers. In this session, we are going to solve several questions on longitudes and latitudes. Answers are available in video format. The questions are very useful to those preparing for KCSE examination.

25 Video Lessons

- Form 4 Chemistry: Radioactivity Questions and Answers
Form 4 Chemistry Radioactivity Questions and Answers. We are going to answer questions on radioactivity. Students preparing for KCSE exams will find these questions very useful.

26 Video Lessons

- Form 4 Energy Changes in Chemical and Physical Processes Questions and Answers
Form 4 Energy Changes in Chemical and Physical Processes Questions and Answers. In this session, we are going to solve several exam standard questions. Answers are available in video format.

39 Video Lessons

- Form 4 Electrochemistry Topical Questions and Answers
In this session, several Form 4 Electrochemistry Questions will be solved. Answers will be given in video format.

52 Video Lessons

- Form 4 Acids, Bases and Salts Topical Questions and Answers
In this session, several questions on acids, bases and salts will be solved. All answers are well explained and in video format. Very ideal for those preparing for KCSE exams.

66 Video Lessons

- Form 4 Matrices and Transformations Questions and Answers
Matrices and Transformations Questions and Video Answers. Several questions have been answered. All answers are in video format.

20 Video Lessons

- Form 4 Chemistry Organic Chemistry II Questions and Answers
Form 4 Chemistry Organic Chemistry II Topical Questions and Answers

57 Video Lessons

- Form 4 Physics Electromagnetic Spectrum Topical Questions and Answers
Form 4 Physics Electromagnetic Spectrum Topical Questions and Answers. In this session, we are going to solve several revision question. All questions have video answers.

15 Video Lessons

- Integration and Its Applications Questions and Answers - Form 4 Calculus
Integration and Its Applications Topical Questions and Answers - Form 4 Calculus In this course, we are going to learn through several revision questions on integration and its applications.

21 Video Lessons

- Form 4 Mathematics Statistics II Questions and Answers
Form 4 Mathematics Statistics II Questions and Answers. Learn through well answered, high quality mathematics questions on Statistics II. Answers are available in video format.

19 Video Lessons

- Blossoms of the Savannah Essay Questions and Answers
Blossoms of the Savannah Essay Questions and Answers. In this session, several questions on Blossoms of the Savannah will be answers.

17 Video Lessons

- Form 4 Oral Literature Revision Questions
Form 4 Oral Literature Revision Questions. In this course, several oral literature revision questions will be tackled.

14 Video Lessons

- Form 4 Physics Uniform Circular Motion Questions and Answers
Form 4 Physics Uniform Circular Motion Questions and Answers. Browse though questions and video solution for the Form 4 Physics topic on uniform circular motion. The answers are detailed and well explained.

20 Video Lessons

- Differentiation and Its Applications Questions and Answers
This course contains many exam standard worked out questions on differentiation and its applications. All the questions have well elaborated video answers with explanations. Most of the questions have been derived from the past KCSE exams. More questions are being added continuously.

20 Video Lessons

- Form 4 Mathematics Lessons on Statistics 2
In this course, we will discuss the following lessons: i) Assumed/working mean. ii) Median, quartiles, deciles and percentiles. iii) Ogive/cumulative frequency curve. iv)Variance and standard deviation.

5 Video Lessons

- Form 4 Matrices and Transformations Lessons
The following areas will be covered in this course: (i) Finding the matrix of transformation given the object and image positions. (ii) Describing the nature of reflection, given the matrix of the reflection. (iii) Describe a given rotation using the matrix of transformation given. (iv)...

7 Video Lessons