Finding area of region with Integration CALC HELP

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^(3x)
y=e^(7x)
x=1

Curves y = e^(3x) and y = e^(7x) intersect at x = 0

Integrate with respect to x
On interval 0 < x < 1, e^(7x) > e^(3x)

Area = ∫₀¹ (e^(7x) − e^(3x)) dx
Area = (1/7 e^(7x) − 1/3 e^(3x)) |₀¹
Area = (1/7 e⁷ − 1/3 e³) − (1/7 − 1/3)
Area = 1/21 (3e⁷ − 7e³ + 4) ≈ 150.157176992

Firstly, sketch the graph. The two graphs intersect at x=0. So you want to know the area between the two curves between x=0 and x=1.

Area= from x=0 to x=1 ʃ(e^(7x) - e^(3x))dx
[1/7e^(7x) - 1/3e^(3x)] =
1/7e^7 - 1/3e^3 - (1/7e^0 - 1/3e^0) = 150.15

Or you can use your calculator:
fnInt(e^(7x)-e^(3x), X, 0, 1 ) = 150.15