Find the arclength of \( y=4 x^{3 / 2} \) on \( 2 \leq x \leq 4 \)

Evaluate the double integral \[ I=\iint_{A} 18 y e^{x^{2}} d x d y \] when \( A \) is the region in the first quadrant bounded by the graphs of \[ x=y^{2}, \quad x=2, \quad y=0 \] 1. \( I=18\left(e^{4}+1\right) \) 2. \( I=\frac{9}{2}\left(e^{4}-1\right) \) 3. \( I=9\left(e^{4}-1\right) \) 4. \( I=\frac{9}{2} e^{4} \) 5. \( I=\frac{9}{2}\left(e^{4}+1\right) \)

\( y = \ln \quad | \sec 2 x ^ { 3 } | \)

\( f^{\prime}(x)=\frac{x^{2}-4}{2 x} \) calcuber \( f^{\prime \prime}(x) \)

\( \lim _ { h \rightarrow 0 } \frac { ( x + n ) ^ { 2 } - x ^ { 2 } } { h } \)

\( f(x)=\left(x^{2}+1\right)^{2} \) es