Question

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

(A) 1

(B) 2

(C) –1

(D) –2

Answer 1

(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`