The diagram shows part of the curve y = e^3x + 1 and the line y = 8. The curve and the line intersect at the point (h, 8).

a. Find h, giving your answer in terms of natural logarithms.

The region R is bounded by the curve, the x-axis, the y-axis and the line x = h.

b. Use integration to show the area of R is 2 +1/3 ln 7.

Transcribed Image Text:

y 8- 2 R 1 y=e³x + 1 -y = 8 h x