Integral of eˣ

By the Fundamental Theorem of Calculus, \int_{-2}^{2} e^{x}\,dx = \Big[e^{x}\Big]_{-2}^{2} = 7.25372.

Differentiate it: the derivative of e^{x} is e^{x}. CalcViz checks every antiderivative this way before showing it.

\int e^{x}\,dx = e^{x} + C

eˣ is its own derivative, so it is also its own antiderivative (plus a constant).

Constant C = 0.0

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Questions students ask

What is the integral of eˣ?

$\int e^{x}\,dx = e^{x} + C$ .

How do you integrate eˣ?

eˣ is its own derivative, so it is also its own antiderivative (plus a constant).

What is the definite integral of eˣ from -2 to 2?

By the Fundamental Theorem of Calculus, $\int_{-2}^{2} e^{x}\,dx = \Big[e^{x}\Big]_{-2}^{2} = 7.25372$ .

How can I check the answer?

Differentiate it: the derivative of $e^{x}$ is $e^{x}$ . CalcViz checks every antiderivative this way before showing it.