Finding the Antiderivative of sec (squared) x

In summary, the conversation discusses finding the antiderivative of sec (squared) x over an interval and the equation for finding the average value. The question posed is what the antiderivative of sec (squared) x is, and also what the derivative of tan x is.
  • #1
softballqt815
1
0

Homework Statement


The average value of sec (squared) x over the interval 0 is less than or equal to x which is less than or equal to pie divided by 4. What is the antiderivative of sec (squared) x?

Homework Equations





The Attempt at a Solution



average value is f(x)dx of (a,b) over b-a. In order to find the area under the curve, the antiderivate of sec (squared) x must be found, and then can be carried out as F(b)-F(a)
 
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  • #2
softballqt815 said:
What is the antiderivative of sec (squared) x?


What is [itex]\frac{d}{dx} \tan x[/itex]?
 

FAQ: Finding the Antiderivative of sec (squared) x

1. What is the formula for finding the antiderivative of sec2 x?

The formula for finding the antiderivative of sec2 x is tan x + C, where C is the constant of integration.

2. How do you solve for the antiderivative of sec2 x?

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.

3. Can you provide an example of finding the antiderivative of sec2 x?

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

4. Are there any special cases when finding the antiderivative of sec2 x?

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.

5. How do you check if you have found the correct antiderivative of sec2 x?

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.

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