Area of the region between the graphs of y = cos(x), y = e^x from x = -3 to x = 0

The calculator will try to find the area bounded by $$$y = \cos{\left(x \right)}$$$, $$$y = e^{x}$$$ from $$$x = -3$$$ to $$$x = 0$$$, with steps shown.

Curves:

Comma-separated. x-axis is $$$y = 0$$$, y-axis is $$$x = 0$$$.

Lower limit:

Optional.

Upper limit:

Optional.

If you are using periodic functions and the calculator cannot find a solution, try to specify the limits. If you don't know the exact limits, specify wider limits that contain the region (see example). Use the graphing calculator to determine the limits.

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Your Input

Find the area of the region bounded by the curves $$$y = \cos{\left(x \right)}$$$, $$$y = e^{x}$$$ from $$$x = -3$$$ to $$$x = 0$$$.

Solution

Some values are found approximately.

$$$\int\limits_{-3}^{-1.292695719373398} \left(\left(e^{x}\right) - \left(\cos{\left(x \right)}\right)\right)\, dx = 1.045201265431511$$$

$$$\int\limits_{-1.292695719373398}^{0} \left(\left(\cos{\left(x \right)}\right) - \left(e^{x}\right)\right)\, dx = 0.236108341859242$$$

Total area: $$$A = 1.281309607290753$$$.

Region bounded by y = cos(x), y = e^x, x = -3, x = 0

Answer

The answer is approximate.

Total area: $$$A = 1.281309607290753$$$A.

Area of the region between the graphs of $$$y = \cos{\left(x \right)}$$$, $$$y = e^{x}$$$ from $$$x = -3$$$ to $$$x = 0$$$

Your Input

Solution

Answer