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AP Calculus AB/BC
Unit 6 – Integration and Accumulation of Change
Topic 6.4
The integral, $\int_{x}^{x^2} \frac{\sin(t)}{t} , dt$ represents the accumulation of the function $\frac{\sin(t)}{t}$ over the interval $[0, x]$. What is the derivative $F'(x)$ of this function?
$\frac{4x^2\sin{x^2}}{x}-\frac{\sin(x)}{x}$
$\frac{4x^2\sin{x^2}}{x^2}-\frac{\sin(x)}{x}$
$\frac{2x\sin{x^2}}{x^2}-\frac{\sin(x)}{x}$
$\frac{\sin{x^2}}{x^2}-\frac{\sin(x)}{x}$
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