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

1 Answer
May 20, 2018

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.