Maharashtra State BoardHSC Arts 12th Board Exam
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if ∫(3x^2+2x+1)dx=14, then α - Mathematics and Statistics

If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`

(A) 1

(B) 2

(C) –1

(D) –2

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Solution

(B) 2

`int_0^alpha (3x^2+2x+1)dx=14`

`[x^3+x^2+x]_0^alpha=14`

`alpha^3+alpha^2+alpha-14=0`

`(alpha-2)(alpha^2+3alpha+7)=0`

But `alpha^2+3alpha+7=0` does not have real roots

`alpha=2`

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