Evaluate the following Integrals:
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)