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NCERT Class XII Mathematics Chapter - - Solutions

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Choose the correct answer in Exercises 21 and 22.
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Question : 22 of 271
Marks: +1, -0
If ddxf(x)=4x3−3x4\frac{d}{dx}f(x)=4x^3-\frac{3}{x^4}, such that f(2)=0f(2)=0. Then f(x)f(x) is
Solution:  
f(x)=∫(4x3−3x4)dxf(x)=\int \left(4x^3-\frac{3}{x^4}\right)dx =4x44−3x−3−3+C=\frac{4x^4}{4}-\frac{3x^{-3}}{-3}+C =x4+1x3+C=x^4+\frac{1}{x^3}+C
∴f(2)=(2)4+1(2)3+C=0\therefore f(2)=(2)^4+\frac{1}{(2)^3}+C=0, C=−16−18=−1298C=-16-\frac{1}{8}=-\frac{129}{8}
∴f(x)=x4+1x3−1298\therefore f(x)=x^4+\frac{1}{x^3}-\frac{129}{8}
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