NCERT Class 12 · Ch 7 Exercise 7.2 · Q22
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 22
Evaluate \(\int \sec^{2}{\left(4 x - 7 \right)}\, dx\).
💡 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: \(\frac{\tan{\left(4 x - 7 \right)}}{4}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=7−4x, du=−4dx.
- An antiderivative is F(x)=\(\frac{\tan{\left(4 x - 7 \right)}}{4}\).
- Differentiate this expression to check that F′(x)=\(\sec^{2}{\left(4 x - 7 \right)}\). Add an arbitrary constant C on each domain component.
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