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Definite Integration question

2024 · 29 Jan · Shift 2 · Q54

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JEE Main
Mathematics
Definite Integration
2024 · 29 Jan · Shift 2 · Q54

Definite Integration question

2024 · 29 Jan · Shift 2 · Q54

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let the slope of the line

45 x+5 y+3=0

be

27 r_1+\frac{9 r_2}{2}

for some

r_1, r_2 \in \mathbb{R}

. Then

\lim_{x \rightarrow 3}\left(\int_3^x \frac{8 t^2}{\frac{3 r_2 x}{2}-r_2 x^2-r_1 x^3-3 x} d t\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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