lim x → 0 ∫ 0 x 2 sin t d t x 3 is equal to:

lim x → 0 + ∫ 0 x 2 sin t d t x 3 = lim x → 0 + sin x 2 x 3 x 2 = lim x → 0 + sin x x × 2 3 = 2 3

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDerivatives (Newton- Leibnitz)Medium2 minPYQ_2021

MathematicsMediumsingle choice

$\lim_{x \to 0} \frac{\int_{0}^{x^{2}} (\sin \sqrt{t}) d t}{x^{3}}$ is equal to:

Answer:

Solution:

$\lim_{x \to 0^{+}} \frac{\int_{0}^{x^{2}} \sin \sqrt{t} d t}{x^{3}} = \lim_{x \to 0^{+}} \frac{(\sin x) 2 x}{3 x^{2}}$

$= \lim_{x \to 0^{+}} (\frac{\sin x}{x}) \times \frac{2}{3} = \frac{2}{3}$

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

⏱ 2mℹ️ Source: PYQ_2021

Loading discussions...