The value of lim x → 0 x s i n x ∫ 0 x 2 s e c 2 t d t is

Lim x → 0 d x d ( x s i n x ) d x d ∫ 0 x 2 s e c 2 t d t = Lim x → 0 s i n x + x c o s x s e c 2 x 2 ⋅ 2 x (by L'Hospital rule) Lim x → 0 ( x s i n x + c o s x ) 2 s e c 2 x 2 = 1 + 1 2 × 1 = 1

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDerivatives (Newton- Leibnitz)Medium2 minPYQ_2003

MathematicsMediumsingle choice

The value of $lim_{x \to 0} \frac{\int _{0}^{x^{2}} s e c ^{2} t d t}{x s i n x}$ is

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$Lim_{x \to 0} \frac{\frac{d}{d x} \int _{0}^{x^{2}} s e c ^{2} t d t}{\frac{d}{d x} ( x s i n x )} = Lim_{x \to 0} \frac{s e c ^{2} x ^{2} \cdot 2 x}{s i n x + x c o s x}$ (by L'Hospital rule) $Lim_{x \to 0} \frac{2 s e c ^{2} x ^{2}}{( \frac{s i n x}{x} + c o s x )} = \frac{2 \times 1}{1 + 1} = 1$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Derivatives (Newton- Leibnitz)

⏱ 2mℹ️ Source: PYQ_2003

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