Encuentre el volumen del solido que está debajo del paraboloide elíptico \( \frac{x^{2}}{4}+\frac{y^{2}}{9}+z=1 \) y arriba del rectángulo \( R=[-1,1] \times[-2,2] \)

Use a Riemann sum to approximate the area under the graph of \( f(x)=4 e^{-x} \) on the interval \( 0 \leq x \leq 1 \) using \( n=5 \) subintervals with the selected points as the right end points. The area is approximately \( \square \) units. (Round to six decimal places as needed.)

7. c) \( \frac{1}{1+x}-\frac{2}{x^{2}-1} \)

1. \( y=\frac{x}{\sqrt[4]{25-x^{2}}} \)

2. \( y=\frac{3^{\sqrt{x}}}{\lg (3-x)} \)

b Hence show that \( \int_{2}^{3} \ln y \mathrm{~d} y=\ln \left(\frac{27}{4 \mathrm{e}}\right) \)