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Q.

The value of ∫01 x2(1−x)9dx is

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a

1610

b

1630

c

1640

d

1660

answer is D.

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Detailed Solution

∫01 x2(1−x)9dx=−∫10 (1−t)2t9dt(1−x=t)=∫01 1−t2−2tt9dt=t1010+t1212−2t111101=110+112−211=1660
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The value of ∫01 x2(1−x)9dx is