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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

  • math -

    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)

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