we are given that
two triangles are similar
so, the ratio of their sides must be same
we get
now, we can solve for x
step-1: Cross multiply both sides
step-2: Simplify left side
step-3: Subtract both sides by 2x
step-4: Divide both sides by 4
so,
............Answer
Integration will be ln | ( x /9 ) + ( ) | + c .
Given ∫ 1 dx / ( - 81 )
Put ,
x = 9 secθ
dx = 9 secθ tanθ dθ
and
= 9 tanθ
Substituting values in ∫ 1 dx / ( - 81 ) ,
∫ (9 secθ tanθ ) dθ / ( 9 tanθ )
∫ secθ dθ = ln | secθ + tanθ | + c
= ln | ( x /9 ) + ( / 9 ) | + c
= ln | ( x /9 ) + ( ) | + c
Hence , the integration will be ln | ( x /9 ) + ( ) | + c .
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