Danh sách tài liệu

• Sketch the region and find its area (if the area is finite): $S = \{(x,y) \mid x \leq 0, 0 \leq y \leq e^x\}$
• Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
  • a. $\int_{-2}^{2} \frac{1}{x^3} dx$
  • b. $\int_{e}^{\infty} \frac{1}{x(\ln x)^p} dx$
• Find the exact length of the curve: $x = \frac{y^4}{8} + \frac{1}{4y^2}$, $1 \leq y \leq 2$.
• The given curve is rotated about the $x$-axis. Find the area of the resulting surface.
• $y = \frac{1}{4}x^2 - \frac{1}{2}\ln x$, $1 \leq x \leq 2$