softballqt815 said:What is the antiderivative of sec (squared) x?
The formula for finding the antiderivative of sec2 x is tan x + C, where C is the constant of integration.
To solve for the antiderivative of sec2 x, you can use the power rule of integration along with the trigonometric identity tan2 x + 1 = sec2 x. This will give you tan x + C.
Sure, if we want to find the antiderivative of sec2 x, we can use the power rule and the trigonometric identity to get the following:
∫ sec2 x dx = ∫ (tan2 x + 1) dx
= ∫ tan2 x dx + ∫ dx
= (tan x) /2 + x + C
= (1/2) tan x + x + C
Yes, when finding the antiderivative of sec2 x, you need to be careful of the domain of the function. Since sec2 x is undefined at x = π/2, you will need to include a constant of integration when integrating in this interval.
To check if you have found the correct antiderivative of sec2 x, you can differentiate it and see if it gives you the original function. In this case, differentiating tan x + C will give you sec2 x, confirming that you have found the correct antiderivative.