Question

What is `f(x) = int 3x-3secx dx` if `f((7pi)/4) = 0`?

Answer 1

`f(x) = 3/2x^2 - 3ln|sec x + tan x| - 49.545`

Explanation:

I assume you mean `f(x) = int (3x - 3 secx)dx`.

So, We have,

`f(x) = int(3x - 3secx) dx`

`= 3int xdx - 3intsec xdx`

`= 3/2x^2 - 3ln|sec x + tan x| + C`

Now, According to the Question,

`color(white)(xxx)f((7pi)/4) = 0`

`rArr 3/2((7pi)/4)^2 - 3ln|sec ((7pi)/4) + tan ((7pi)/4)| + C = 0`

`rArr 3/2(22/4)^2 - 3ln|(-1/4) + 0| + C = 0`

`rArr 3/2 * 121/4 - 3(-1.39) + C = 0` [As `ln(1/4) = -1.39` (approx)]

`rArr 49.545 + C = 0` [Using Calculator]

`rArr C = -49.545`

So, `f(x) = 3/2x^2 - 3ln|sec x + tan x| - 49.545`

Hope this helps.