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Let $f : R \to R$ be defined by $f (x) = \int_{0}^{1} \frac{x^{2} + t^{2}}{2 - t} d t$
Then the curve $y = f (x)$ is

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an ellipse

a straight line

a parabola

a hyperbola

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detailed solution

Correct option is C

f(x)=x2∫01 dt2−t+∫01 t22−tdt=−x2log |2−t|01+∫01 −t−2+42−tdty=x2log 2+−12−2+4log 2which represent a parabola.

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Let f:R→R be defined by f(x)=∫01 x2+t22−tdtThen the curve y=f(x) is

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Ready to Test Your Skills?

free study material

Let $f : R \to R$ be defined by $f (x) = \int_{0}^{1} \frac{x^{2} + t^{2}}{2 - t} d t$
Then the curve $y = f (x)$ is