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

So, We have,

Now, According to the Question,

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To find ( f(x) = \int (3x - 3\sec x) , dx ) if ( f\left(\frac{7\pi}{4}\right) = 0 ), we first integrate ( 3x - 3\sec x ) with respect to ( x ):

[ \int (3x - 3\sec x) , dx = \frac{3}{2}x^2 - 3\ln|\sec x + \tan x| + C ]

Now, plug in ( x = \frac{7\pi}{4} ):

[ f\left(\frac{7\pi}{4}\right) = \frac{3}{2}\left(\frac{7\pi}{4}\right)^2 - 3\ln|\sec\left(\frac{7\pi}{4}\right) + \tan\left(\frac{7\pi}{4}\right)| + C ]

Given that ( f\left(\frac{7\pi}{4}\right) = 0 ), we can solve for ( C ):

[ 0 = \frac{3}{2}\left(\frac{49\pi^2}{16}\right) - 3\ln|-\sqrt{2} - 1| + C ] [ C = 3\ln|-\sqrt{2} - 1| - \frac{147\pi^2}{32} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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