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Evaluate lim(x->0) [∫(0 to x 2 ) sin(t) 1/2 dt/ x 3 ]

Evaluate
lim(x->0) [∫(0 to x2) sin(t)1/2 dt/ x3]

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \lim_{x\rightarrow 0}\frac{\int_{0}^{x^2}sin\sqrt{t}dt}{x^3}
It is 0/0 form. Apply L’hospital rule
I = \lim_{x\rightarrow 0}\frac{sin\sqrt{x^2}.2x}{3x^2}
I = \lim_{x\rightarrow 0}\frac{2sinx}{3x}
I = \frac{2}{3}\lim_{x\rightarrow 0}\frac{sinx}{x}
I = \frac{2}{3}

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