Problem 48
State the method of integration you would use to perform each integration. Explain why you chose that method. Do not integrate.
(a) \(\int x \sqrt{x^{2}+1} d x\)
(b) \(\int x^{2} \sqrt{x^{2}-1} d x\)
Text Transcription:
int x sqrt{x^2 + 1} dx
int x^2 sqrt{x^2 - 1} dx
Step-by-Step Solution:
Step 1 of 5) The spherical wedge closely approximates a cube of these dimensions when rk , fk , and uk are all small (Figure 14.52). It can be shown that the volume of this spherical wedge Vk is Vk = rk 2 sin fk rk fk uk for (rk , fk , uk), a point chosen inside the wedge. The corresponding Riemann sum for a function ƒ(r, f, u) is
Step 2 of 2
