MENU
Educational Resources
Exam Papers
Form 1 Videos
Form 2 Videos
Form 3 Videos
Form 4 Videos
Grade 4 Videos
Grade 5 Videos
Grade 6 Videos
Grade 7 Videos
Class 8 Videos
Form 1 Exams
Form 2 Exams
Form 3 Exams
Form 4 Exams
KCSE Videos
Class 8 Exams
Grade 5 Exams
Grade 4 Exams
Grade 3 Exams
Grade 2 Exams
Grade 1 Exams
Online Tests
Online Tuition
Sign In
Join
Get access to thousands of educational resources
Get premium membership
and access revision papers with marking schemes, video lessons and live classes.
OR
Processing. Please wait.
Form 4 Mathematics area and approximation: Integration questions and answers
Determine the area bounded by the curve #y=x^2 - 4#, the x-axis and the line x=4.
(3m 5s)
4368 Views
SHARE
|
« Previous
Next »
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).
2.
Determine the area bounded by the curve #y=x^2 - 4#, the x-axis and the line x=4.
3.
Find the area enclosed by the curve #y=4x-x^2#, the x-axis and the lines x=1 and x=2.
4.
Find the area bounded by the curve #y=2x^3-5#, the x-axis and the lines x=2 and x=4.
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.
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.
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.
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
9.
Evaluate #int _2^4 x^2 + 2x - 15\ dx#
10.
Find the value of k if #int_0^2(kx^3 – 3x^2)dx=16#
×
Share Content Via:
Facebook
Twitter
WhatsApp
Close
Get premium membership