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Chapter 10: Q 32 (page 777)

Find a function fthat has the given derivative f'and value f(c)

f'x=2xsecx2tanx2,f0=2

Short Answer

Expert verified

The anti derivative issecx2+2

Step by step solution

01

Given information 

The given expression isf'x=2xsecx2tanx2,f0=2

02

Simplification

Given f'x=2xsecx2tanx2,f0=2

We will use an intelligent guess-and-check method to find f

Here secx2tanx2is a derivative of secx2

So our guess can be secx2

Now, 2xis a derivative of x2

Hence we can say that

fx=secx2+c

Now,

f0=2

鈬�2=sec0+c

localid="1660720299977" 鈬�2=1+c鈬�c=2-1鈬�c=1

Hence the antiderivative is sec2x+1

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