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# Find the area between y = e^{x} and y = e^{-x} and x = 1?

**Solution:**

Given y = e^{x} and y = e^{-x} and x = 1

In order to find area, we need to solve the two given equation

Since both equations are equal to ‘y’. We can equate them to get x value

e^{x} = e^{x}

e^{x} - e^{x }= 0

e^{x} - 1/e^{x }= 0

e^{2x} - 1/e^{x} = 0

e^{2x} - 1 = 0

e^{2x} = 1

Apply ‘ln’ on both sides

2xlne = ln1

2x = 0

x = 0

The horizontal line is the x-axis, the vertical line is the y-axis

The orange curve is y = e^{x}

The blue curve is y = e^{-x}

The green line is x = 1

So, we determine the area of y = e^{x} in the interval 0 ≤ x ≤ 1 and then subtract the area of y = e^{-x} in the interval 0 ≤ x ≤ 1

Area = ∫\(_ 0^1\) (e^{x }- e^{-x})dx

Area = e^{x }+ e^{-x} | \(_ 0^1\)

Area = e^{1} + 1/e - (1 + 1)

Area = -2 + 1/e + e

Area = -2 + 2.71 + 1/(2.71)

Area = 1.086 sq units

## Find the area between y = e^{x} and y = e^{-x} and x = 1?

**Summary:**

The area between y = e^{x} and y = e^{-x} and x = 1 is 1.086 sq.units

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