# What is #f(x) = int sec^2x- cosx dx# if #f((5pi)/4) = 0 #?

These are known integrals:

therefore,

Therefore,

By signing up, you agree to our Terms of Service and Privacy Policy

To find the integral of ( \int (\sec^2 x - \cos x) , dx ), we first need to integrate each term separately. The integral of ( \sec^2 x ) is ( \tan x ), and the integral of ( \cos x ) is ( \sin x ). Thus, the integral of ( \sec^2 x - \cos x ) is ( \tan x - \sin x + C ), where ( C ) is the constant of integration.

Given that ( f\left(\frac{5\pi}{4}\right) = 0 ), we can substitute ( x = \frac{5\pi}{4} ) into the expression for ( f(x) ) and solve for the constant ( C ).

( f\left(\frac{5\pi}{4}\right) = \tan\left(\frac{5\pi}{4}\right) - \sin\left(\frac{5\pi}{4}\right) + C = 0 )

Using the trigonometric values for ( \tan\left(\frac{5\pi}{4}\right) ) and ( \sin\left(\frac{5\pi}{4}\right) ), we get:

( (-1) - \left(-\frac{\sqrt{2}}{2}\right) + C = 0 )

Simplifying:

( -1 + \frac{\sqrt{2}}{2} + C = 0 )

( C = 1 - \frac{\sqrt{2}}{2} )

So, ( f(x) = \tan x - \sin x + 1 - \frac{\sqrt{2}}{2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7