help me pls (2U Math) (1 Viewer)

sodiumziha · Jul 17, 2018

Stupid question but how do you integrate secx x tanx

apparently the answer's secx?????

Can someone explain this in like a REALLY simple way cause idek

HeroWise · Jul 17, 2018

u substitution

Let u be secx and you find that if you differentiate secx you can secxtanx

from there you can just continue the u sub or end it stating

$\frac{d}{dx}(secx)=secxtanx$

$\int d(secx)= \int secxtanx $ dx$$

$The d and integral symbol cancels as they are opposite of each other and you get$

$secx=\int secxtanxdx$

fan96 · Jul 17, 2018

The key is just to know that the derivative of $\sec x$ is $\sec x \tan x$ and hence the integral of $\sec x \tan x$ must be $\sec x$ plus a constant (since differentiation and integration are roughly opposites of each other).

You could naturally derive the answer using a substitition but I don't believe this is within the scope of the 2U course.

In fact it helps to know the derivative of all the trig functions:

$\frac{d}{dx} \sin x = \cos x$

$\frac{d}{dx} \cos x =- \sin x$

$\frac{d}{dx} \tan x = \sec^2x$

$\frac{d}{dx} \sec x = \sec x\tan x$

$\frac{d}{dx}\,$cosec$\,x = -\,$cosec$\,x \cot x$

$\frac{d}{dx} \cot x = -\,$cosec$^2x$

Although the last three shouldn't show up in the 2U course often.

help me pls (2U Math) (1 Viewer)

sodiumziha

Member

HeroWise

Active Member

fan96

617 pages

Users Who Are Viewing This Thread (Users: 0, Guests: 1)