## dakotajason27 3 years ago Evaluate the integral! From 0 to pi/3 of 4sec x tan x dx

1. dakotajason27

$\int\limits_{0}^{\pi/3} 4\sec x \tan x$

2. coolestkidd

i am helpi u right noe

3. dakotajason27

Like i get the basic jist of integrals i just get stuck on finding the antiderivative

4. coolestkidd

oka

5. anonymous

see if you can think of a function whose derivative is $$\sec(x)\tan(x)$$

6. anonymous

or look in the book for the derivatives of trig functions. you will see it

7. coolestkidd

i cant find the anser

8. dakotajason27

sec 4x and they just applied the chasin rule?

9. dakotajason27

chain*

10. anonymous

easier than that

11. anonymous

if you take the derivative of $$\sec(4x)$$ you will get $$4\sec(4x)\tan(4x)$$ which is not at all what you want. just leave the constant alone and take $$4\sec(x)$$

12. anonymous

plug in $$\frac{\pi}{3}$$ plug in $$0$$ and subtract actually forget 0 because $$\tan(0)=0$$

13. dakotajason27

ok perfect i can do it from here thanks :)

14. anonymous

yw

15. dakotajason27

16. coolestkidd

yes