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Definite Integration question

2024 · 1 Feb · Shift 2 · Q55

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JEE Main
Mathematics
Definite Integration
2024 · 1 Feb · Shift 2 · Q55

Definite Integration question

2024 · 1 Feb · Shift 2 · Q55

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f:(0, \infty) \rightarrow \mathbf{R}

and

\mathrm{F}(x)=\int\limits_0^x \mathrm{t} f(\mathrm{t}) \mathrm{dt}

. If

\mathrm{F}\left(x^2\right)=x^4+x^5

, then

\sum\limits_{\mathrm{r}=1}^{12} f\left(\mathrm{r}^2\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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