NCERT Class 12 · Ch 7 Exercise 7.9 · Q10
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.9 Question 10
If f(x)=∫₀ˣ t sin t dt, find f′(x).
💡 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: B: x sin x.
- The integrand t sin t is continuous for every real t.
- The first fundamental theorem of calculus gives f′(x) equal to the integrand at its upper limit: x sin x.
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