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Suppose that F (x) is an antiderivative ...

Suppose that F (x) is an antiderivative of `f (x)=sinx/x,x>0` , then `int_1^3 (sin2x)/x dx` can be expressed as

A

`F(6)-F(2)`

B

`1/2(F(6)-F(2))`

C

`1/2(F(3)-F(1))`

D

`2(F(6)-F(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int_(1)^(3)(sin 2x)/x dx`
Put `2x=t` and `dx=(dt)/2`
`:. I=2/2 int_(2)^(6) (sint)/t dt =int_(2)^(6) (sint)/t dt`
But gien `int(sinx)/x dx=F(x)`
or `int_(2)^(6)(sint)/t dt =F(6)-F(2)`
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