1.
-
+
1.
+The Power Rule for derivatives states:
-
-2.
-
+
2.
+The Power Rule for antiderivatives states:
-
-3.
-
-
Practice with the following derivatives:
-
-\begin{align*}
-\frac{d}{dx}\left( 2x^2 + x^{-3} + 4\sqrt{x} \right) \amp = \\
-\frac{d}{dx}\left( \frac{1}{x} + 3e^{2x} + x^e + \pi^e \right) \amp =
-\end{align*}
+
+
3.
+Practice with the following derivatives:
+
(a)
+
+\(\displaystyle \frac{d}{dx}\left( 2x^2 + x^{-3} + 4\sqrt{x} \right) = \)
-
+
+(b)
+
+\(\displaystyle \frac{d}{dx}\left( \frac{1}{x} + 3e^{2x} + x^e + \pi^e \right) = \)
-4.
-
-
Practice with the following antiderivatives:
-
-\begin{align*}
-\int 2x^2 + x^{-3} + 4\sqrt{x} \ dx \amp = \\
-\int \frac{1}{x} + 3e^{2x} + x^e + \pi^e \ dx \amp =
-\end{align*}
+
+
+
-4.
+Practice with the following antiderivatives:
+
(a)
+
+\(\displaystyle \int 2x^2 + x^{-3} + 4\sqrt{x} \ dx = \)
-
+
+(b)
+
+\(\displaystyle \int \frac{1}{x} + 3e^{2x} + x^e + \pi^e \ dx = \)
-+ +
Theorem 1. Fundamental Theorem of Calculus.
@@ -237,22 +241,24 @@ eBookConfig.enable_chatcodes = false;
\int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a).
\end{gather*}
-If \(f(x)\) is a probability density function (donβt worry about what that means for now), then integrals such as \(\int_a^b f(x)\ dx\) are used to calculate certain probabilities, and so are function values of the form \(F(x)\text{.}\)
-
5.
-
-
Practice with the following integrals:
-
-\begin{align*}
-\int_0^1 \frac{3}{2} x^{3/2} \ dx \amp = \\
-\int_0^x 3e^{-3t} \ dt \amp =
-\end{align*}
+
+
If \(f(x)\) is a probability density function (donβt worry about what that means for now), then integrals such as \(\int_a^b f(x)\ dx\) are used to calculate certain probabilities, as are values of the form \(F(x)\text{.}\)
-
+5.
+Practice with the following integrals:
+
(a)
+
+\(\displaystyle \int_0^1 \frac{3}{2} x^{3/2} \ dx = \)
-(b)
+
+\(\displaystyle \int_0^x 3e^{-3t} \ dt = \)
+
+
+