NCERT Class 12 · Ch 7 Exercise 7.1 · Q22
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.1 Question 22
Find f if f′(x)=4x³−3/x⁴ and f(2)=0.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: A: f(x)=x⁴+1/x³−129/8 on x>0.
- Work on each open interval where the original integrand is real and defined.
- Integrate to get f=x⁴+x^(−3)+C.
- The condition f(2)=0 gives C=−16−1/8=−129/8.
- An antiderivative is F(x)=\(x^{4} - \frac{129}{8} + \frac{1}{x^{3}}\).
- Differentiation verifies the given derivative. The prescribed value fixes the constant, so no arbitrary constant remains.
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