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GO Classes DPP | GATE CS, DA | Calculus & Optimization | Initial Value Integration

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Find $f(x)$ if $f'(x)=6x^2+\sec^2 x$ and $f(0)=4$.

  1. $f(x)=2x^3+\tan x+4$
     
  2. $f(x)=2x^3-\tan x+4$
     
  3. $f(x)=6x^3+\tan x+4$
     
  4. $f(x)=2x^3+\tan x-4$

1 Answer

1 1 vote

Since $f'(x)=6x^2+\sec^2 x$, integrate both sides.

$$\Rightarrow f(x)=\int(6x^2+\sec^2 x)dx$$

$$\Rightarrow f(x)=2x^3+\tan x+C$$

Now use $f(0)=4$.

$$\Rightarrow f(0)=2(0)^3+\tan0+C$$

$$\Rightarrow 4=0+0+C$$

$$\Rightarrow C=4$$

$$\boxed{\therefore {f(x)=2x^3+\tan x+4}}$$

Answer: A.

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