Q. 85.0( 2 Votes )

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Answer :

Given Definite Integral can be written as:


……(1)


Let us assume y = logx


Differentiating w.r.t x on both sides


d(y) = d(logx)


……(2)


Upper limit for the Definite Integral:


x = 3 y = log(3)


y = log3……(3)


Lower limit for the Definite Integral:


x = 1 y = log(1)


y = 0……(4)


Substituting (2),(3),(4) in the eq(1) we get,



We know that ∫ cos x dx = sin x + c



We know that:


here f’(x) is derivative of f(x))


I(x) = sin(log3) – sin(0)


I(x) = sin(log3) – 0


I(x) = sin(log3)



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