If d/dx[G(x) = etanx/x, x belongs to (0,pi/2), then ∫(2/x)etan(x2)dx ( limit from 1/4 to 1/2) is equal to a - Maths - Integrals

Question

If d/dx[G(x) = etanx/x, x belongs to (0,pi/2), then
∫(2/x)etan( x2 )dx
( limit from 1/4 to 1/2) is equal to
a G(1/(2)1/2) - G(1/2)
b pi[G(1/2) - G(1/4)]
c G(pi/4) - G(pi/16)
d 2[G(pi/4) - G(pi/16)]

Dev Kumar · Answer

To all those who are having problem in above question
find the solution given below useful, this is the easiest method to
solve the given question

NOTE : The above question is solved keeping in mind that
student know the basic property of Integration &
derivative-antiderivative

Hope all your queries get cleared after referring the above
solution

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If d/dx[G(x) = etanx/x, x belongs to (0,pi/2), then ∫(2/x)etan( x2 )dx ( limit from 1/4 to 1/2) is equal to a. G(1/(2)1/2) - G(1/2) b. pi[G(1/2) - G(1/4)] c. G(pi/4) - G(pi/16) d. 2[G(pi/4) - G(pi/16)]

If d/dx[G(x) = e^tanx/x, x belongs to (0,pi/2), then ∫(2/x)e^tan( ^x² ⁾dx ( limit from 1/4 to 1/2) is equal to

a. G(1/(2)^1/2) - G(1/2)

b. pi[G(1/2) - G(1/4)]

c. G(pi/4) - G(pi/16)

d. 2[G(pi/4) - G(pi/16)]