NCERT Class 12 · Ch 7 Exercise 7.2 · Q4
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 4
Evaluate \(\int \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}\, dx\).
💡 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: \(\cos{\left(\cos{\left(x \right)} \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=cos x, du=−sin x dx; integrate −sin u du.
- An antiderivative is F(x)=\(\cos{\left(\cos{\left(x \right)} \right)}\).
- Differentiate this expression to check that F′(x)=\(\sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}\). Add an arbitrary constant C on each domain component.
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