Integration Questions and Answers

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. 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