AP EAMCET · Maths · Indefinite Integration
If \(\int x^2 \cos ^2 x d x=\frac{1}{6} f(x)+g(x) \sin 2 x+h(x) \cos 2 x+c\) then \(\mathrm{f}(1)+\mathrm{g}(2)+\mathrm{h}\left(\frac{1}{2}\right)=\)
- A 0
- B 2
- C 1
- D -1
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(\int x^2 \cos ^2 x d x = \int x^2 \frac{1+\cos 2x}{2} dx = \frac{1}{2}\int x^2 dx + \frac{1}{2}\int x^2 \cos 2x dx\) \(= \frac{1}{2}\frac{x^3}{3} + \frac{1}{2} \left[ x^2 \frac{\sin 2x}{2} - \int 2x \frac{\sin 2x}{2} dx \right]\)…
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