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Grade 12th passIntegral Calculus

in[0,2] f(x) and g(x) are differentiable functions with f`(1)=2, g`(1)=4 ,f(2)=3 ,g(2)=9 then at x=3/2 find value of f(x)-g(x)

Ohidul

8 Years agoGrade 12th pass

1 Answer

Pradeep Tangirala

8 Years ago

f'(1)=2 so...f'(x) = 2x (say)

Integrating on both sides...

So f(x)=2x + C

Where C is some constant that we can find...

But f(2)=3

So f(2)=2×2 +c

4+C=3

C=-1

So...f(x)= 2x-1

f(3/2)=2×3/2 - 1

=2

Similarly....g(x)=4x + k

g(2)=9

So...K=1

g(x)=4x+1

g(3/2)=4×3/2 +1

=7

So...f(x) - g(x) = 2-7 =-5

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