Find a function f such that f‴(x)=11+sin2x. (This problem is supposed to be easy; don't misinterpret the word "find".)

If f′(x)=g(x) then f(x)=∫g(x)dxThus,(f″(x))′=11+sin2(x)f″(x)=(1)∫11+sin2+(x)dxThe above equation, can be written as:(f′(x))′=∫11+sin2(x)dxSo,f′(x)=(1)∫∫11+sin2(x)dxdxNow, from (1) we getf(x)=∫∫∫11+sin2(x)dxdxdx

"Find a function f such that f‴(x)=11+sin2x. (This..." was answered by our community

Secondary
Math Word Problem

Jaya Legge

Answered question

2021-06-25

Find a function f such that

f^{‴} (x) = \frac{1}{\sqrt{1 + \sin^{2} x}}

. (This problem is supposed to be easy; don't misinterpret the word "find".)

Answer & Explanation

Willie

Skilled2021-06-26Added 95 answers

f^{'} (x) = g (x) t h e n f (x) = \int g (x) d x

Thus,

{(f^{″} (x))}^{'} = \frac{1}{\sqrt{1 + \sin^{2} (x)}}

f^{″} (x) =^{(1)} \int \frac{1}{\sqrt{1 + \sin^{2} + (x)}} d x

The above equation, can be written as:

{(f^{'} (x))}^{'} = \int \frac{1}{\sqrt{1 + \sin^{2} (x)}} d x

So,

f^{'} (x) =^{(1)} \int \int \frac{1}{\sqrt{1 + \sin^{2} (x)}} d x d x

Now, from (1) we get

f (x) = \int \int \int \frac{1}{\sqrt{1 + \sin^{2} (x)}} d x d x d x

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