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Question

Find the area of the figure bounded by the following curves
Find all values of a for which the inequality a0xdxa+4 is satisfied.

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Solution

a0x dxa+4

x22|a0a+4

a22a+4

a22a+8
a22a80
a24a+2a90
a(a4)+2(a4)0
(a+2)(a4)0
Compute the signs : -
(i) a2
a<2:(a+2)(a4)>0
a=2:(a+2)(a4)=0
(ii) 2<a<4
(a+2)(a4)<
(iii) a4
a=5:(a+2)(a4)=0
a>4:(a+2)(a4)>0
Choosing the ranges that satisfy the required condition :-
Solution : - 2a4.

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