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Q22   Choose the correct answer   The anti derivative of  

           If   \frac{d}{dx}f(x) = 4 x ^3 - \frac{3}{x^4}  such that f (2) = 0. Then f (x) is

       A ) x ^ 4 + \frac{1}{x^3} - \frac{129 }{8} \\\\ B ) x ^ 3 + \frac{1}{x^4} - \frac{129 }{8} \\\\ C ) x ^ 4 + \frac{1}{x^3} + \frac{129 }{8}\\\\ D) x ^ 3 + \frac{1}{x^4} - \frac{129 }{8}

Answers (1)

best_answer

Given that the anti derivative of \frac{d}{dx}f(x) = 4 x ^3 - \frac{3}{x^4}

So, \frac{d}{dx}f(x) = 4 x ^3 - \frac{3}{x^4}

f(x) = \int 4 x ^3 - \frac{3}{x^4}\ dx

f(x) = 4\int x ^3 - 3\int {x^{-4}}\ dx

f(x) = 4\left ( \frac{x^4}{4} \right ) -3\left ( \frac{x^{-3}}{-3} \right )+C

f(x) = x^4+\frac{1}{x^3} +C

Now, to find the constant C;

we will put the condition given, f (2) = 0

f(2) = 2^4+\frac{1}{2^3} +C = 0

16+\frac{1}{8} +C = 0

or C = \frac{-129}{8}  

\Rightarrow f(x) = x^4+\frac{1}{x^3}-\frac{129}{8}

Therefore the correct answer is A.

Posted by

Divya Prakash Singh

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