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

Ans:Hello Student,Please find answer to your question belowIt is 0/0 form. Apply L’hospital rule

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Grade 12Integral Calculus

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

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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
$I = \lim_{x\rightarrow 0}\frac{sin\sqrt{x^2}.2x}{3x^2}$
$I = \lim_{x\rightarrow 0}\frac{2sinx}{3x}$
$I = \frac{2}{3}\lim_{x\rightarrow 0}\frac{sinx}{x}$
$I = \frac{2}{3}$