math
posted by Anonymous on .
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=e^1x, y=e^4x, x=1

wrt x:
∫[0,1] e^(4x)e^x dx
= 1/4 e^(4x)  e^x [0,1]
= (1/4 e^4  e)  (1/4  1)
= 1/4 (3 + e^4  4e)
wrt y:
∫[1,e] lny  1/4 lny dy + ∫[e,e^4] 1 1/4 lny dy
= (3/4) + (1/4 (e$4  4e))
= 1/4 (3 + e^4  4e)