Calculating the Area Under the Curve | The Integral of e^x dx explained

Integral of: e^x dx

The integral of e^x dx represents the area under the curve of the function y = e^x

The integral of e^x dx represents the area under the curve of the function y = e^x.

To evaluate this integral, we can use the power rule for integration. The power rule states that the integral of x^n dx, where n is a constant, is (1/(n+1)) * x^(n+1) + C (where C is the constant of integration).

In the case of e^x, the power rule is not directly applicable because the exponent does not depend on x. Instead, we can use a special property of the exponential function, which is that its derivative with respect to x is equal to itself. That is, d/dx (e^x) = e^x.

Using this property, we can conclude that the integral of e^x dx is simply e^x + C, where C is the constant of integration.

So, the integral of e^x dx is e^x + C.

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