The anti – derivative of the function (3x + 4) |sin x|, when 0 < x < π , is given by Options: A . &nbsp 3 s i n x − ( 3 x + 4 ) c o s x + c B . &nbsp 3 s i n x + ( 3 x + 4 ) c o s x + c C . &nbsp − 3 s i n x − ( 3 x + 4 ) c o s x + c D . &nbsp None of these

The anti – derivative of the function (3x + 4) |sin x|, when 0<x<

Question -

The anti – derivative of the function (3x + 4) |sin x|, when $0 < x < π$ , is given by

Options:

A .

3 s i n x - (3 x + 4) c o s x + c

B .

3 s i n x + (3 x + 4) c o s x + c

C .

- 3 s i n x - (3 x + 4) c o s x + c

D . None of these

Answer: Option A
:
A
In the interval

(0, π)

, sin x is positive, therefore,

(3 x + 4) | s i n x | = (3 x + 4) s i n x

∴

The antiderivative of

(3 x + 4) | s i n x |

= \int (3 x + 4) s i n x d x = - (3 x + 4) c o s x + \int 3 c o s x d x = - (3 x + 4) c o s x + 3 s i n x + c

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