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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.

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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

 

 

 

Image From EcoleBooks.com3.  Find the values of a which satisfy the integral

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Image From EcoleBooks.com    (x2 + 1) dx = 2a  

 

 

Integration Answers

1

 

a)

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X = 1 or x = -3

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b)

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c)

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d)

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Image From EcoleBooks.com units

 

M1

 

A1

 

B1

B1

 

 

 

M1

M1

 

 

 

 

A1

 

 

M1

 

A1

 

 

 

B1

 

Diagram

   

10

 

 

1.  S10 = 100


52
(x-1) (x-2) dx

x – 2

=
52x – 1dx

=
x2/2 – x 52

2.  


 (x2 + 1) dx = 2a  

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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


 




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