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Integration Questions/problems
1. The diagram below, not drawn to scale shows part of the curve y = x2+5 and the line y = 8-2x. The line intersects the curve at points C and D. Lines AC and BD are parallel to the y-axis.
a) Determine the coordinates of C and D (4 mks)
b) Use integration to calculate the area bounded by the curve and the x- axis between the points C and D (3 mks)
c) Calculate the area enclosed by the lines CD, CA, BD and the x-axis (2 mks)
d) Hence determine the area of the shaded region (1 mk)
2. Evaluate:-
x2 – 3x + 2 dx
x – 2
3. Find the values of a which satisfy the integral
(x2 + 1) dx = 2a
Integration Answers
1 | a) X = 1 or x = -3 b) c) d) |
M1
A1
B1 B1
M1 M1
A1
M1
A1
B1 |
Diagram | |
10 |
units
1. S10 = 100
52
(x-1) (x-2) dx
x – 2
=
52x – 1dx
=
x2/2 – x 52
2.
(x2 + 1) dx = 2a
x3 + x = 2a
3 1
a3+ a – 0 =2a
3 1
a3 + 3a= 6a
a3 = 3a
(a3 – 3a) = 0
a(a2 – 3) = 0
a = 0
or 3 = ± 1.732
