Find the antiderivative of fx given by f x -4 x 3 - 3 - x 4 such that f2-0

→ let f(x) = ∫ 4x^3 3/x^4dx = 4(x^44) 3(x^ 3 3)+C = x^4+1x^3+C Given F(2) = 0 ⇒ 0 = 16+18+C ⇒ C = (128+18) = 1298 ⇒ F ...

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Standard XII

Mathematics

Definition of Function

Find the anti...

Question

Find the antiderivative of f(x) given by $f (x) = 4 x^{3} - \frac{3}{x^{4}}$ such that f(2)=0

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Solution

$\to$ let $f (x) = \int 4 x^{3} - \frac{3}{x^{4}} d x$
$= 4 (\frac{x^{4}}{4}) - 3 (\frac{x^{- 3}}{- 3}) + C$
$= x^{4} + \frac{1}{x^{3}} + C$
Given $F (2) = 0$
$\Rightarrow 0 = 16 + \frac{1}{8} + C$
$\Rightarrow C = - (\frac{128 + 1}{8}) = \frac{- 129}{8}$
$\Rightarrow F (x) = x^{4} + \frac{1}{x^{3}} - \frac{129}{8}$

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Find the antiderivative of f(x) given by f(x)=4x3−3x4 such that f(2)=0

→ let f(x)=∫4x3−3x4dx=4(x44)−3(x−3−3)+C=x4+1x3+CGiven F(2)=0⇒0=16+18+C⇒C=−(128+18)=−1298⇒F(x)=x4+1x3−1298

Find the antiderivative of f(x) given by $f (x) = 4 x^{3} - \frac{3}{x^{4}}$ such that f(2)=0