NCERT Class 12 · Ch 7 Exercise 7.4 · Q25
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.4 Question 25
Evaluate \(\int \frac{1}{\sqrt{- 4 x^{2} + 9 x}}\, dx\).
💡 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: \(\frac{\operatorname{asin}{\left(\frac{8 x}{9} - 1 \right)}}{2}\) + C.
- Work for 0<x<9/4.
- Complete the square: 9x−4x²=[81−(8x−9)²]/16; set u=(8x−9)/9.
- An antiderivative is F(x)=\(\frac{\operatorname{asin}{\left(\frac{8 x}{9} - 1 \right)}}{2}\).
- Differentiate this expression to check that F′(x)=\(\frac{1}{\sqrt{- 4 x^{2} + 9 x}}\). Add an arbitrary constant C on each domain component.
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