Let $f(x)=x^2+a x+b$ and the only solution of the equation $f(x)=$ minimum $f(x)$ is $x=0$ and $f(x)=0$ has root $\alpha$ and $\beta$, then $\int_\alpha^\beta x^3 d x$ is equal to

$\frac{1}{4}\left(\beta^4+\alpha^4\right)$

$\frac{1}{4}\left(a^2-b^2\right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

f(x)=x^2+a x+b

and the only solution of the equation

f(x)=

minimum

f(x)

x=0

and

f(x)=0

has root

\alpha

and

\beta

, then

\int_\alpha^\beta x^3 d x

is equal to

View answer and explanation

Correct option: C

Option C (0) is correct because the integral of an odd function over a symmetric interval is zero.

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