Question

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Answer 1

$\textbf{Answer :}$

Now,

∫ x^2 sin2x dx

= x^2 ∫ sin2x dx -
∫ { d/dx (x²) × ∫ sin2x dx } dx + c,

where c is integral constant

= - 1/2 x² cos2x -
∫ { 2x (- 1/2) cos2x } dx + c

= - 1/2 x² cos2x + ∫ x cos2x dx + c

= - 1/2 x² cos2x + x ∫ cos2x dx -
∫ { d/dx (x) × ∫ cos2x dx } dx + c

= - 1/2 x² cos2x + 1/2 x sin2x
- 1/2 ∫ sin2x dx + c

= - 1/2 x² cos2x + 1/2 x sin2x
- 1/2 ( - 1/2 cos2x ) + c

= - 1/2 x² cos2x + 1/2 x sin2x + 1/4 cos2x + c,

which is the required solution.

Therefore, $\textbf{Option (b)}$ is correct.

#$\bold{MarkAsBrainliest}$

Answer 2

Answer:

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