NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 10

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. Factor sin⁸−cos⁸=(sin⁴−cos⁴)(sin⁴+cos⁴). The denominator is sin⁴+cos⁴, leaving sin²−cos²=−cos 2x.
3. An antiderivative is F(x)=\(- \frac{\sin{\left(2 x \right)}}{2}\).
4. Differentiate this expression to check that F′(x)=\(\frac{\sin^{8}{\left(x \right)} - \cos^{8}{\left(x \right)}}{- 2 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 1}\). Add an arbitrary constant C on each domain component.