Suppose that `F(x)` is an anti-derivative of `f(x)=(sinx)/x ,w h e r ex > 0.` Then `int_1^3tan^(-1)dx` can be expressed as `F(6)-F(2)` (b) `1/2(F(6)-f(2))` `1/2(F(3)-f(1))` (d) `2(F(6))-F(2))`

Options

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))`

Answer

A

Explanation

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)`