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

Lovey , 10 Years ago
Grade 12
anser 1 Answers
Jitender Singh

Last Activity: 10 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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