Chapter 29

Integrate $$\int \sin 3 x \, d x$$

Find the average ordinate for each function in the given interval. $$y=x^{2} \quad \text { from } 0 \text { to } 6$$

Derivative of \(b^{u}\). Differentiate. $$y=3^{2 x}$$

Exponential Functions $$\int a^{5 x} d x$$

Find the derivative. $$y=x \sin ^{-1} x$$

Find the derivative. $$y=\tan 2 x$$

First Derivatives Find the derivative. $$y=\sin x$$

Differentiate. $$y=\log x^{-2}$$

Integrate $$\int \cos 7 x \, d x$$

Exponential Functions $$\int a^{9 x} d x$$

Find the average ordinate for each function in the given interval. $$y=x^{3} \quad \text { from }-5 \text { to } 5$$

Derivative of \(b^{u}\). Differentiate. $$y=10^{2 x+3}$$

Find the derivative. $$y=\sin ^{-1} \frac{x}{a}$$

Find the derivative. $$y=\sec 4 x$$

First Derivatives Find the derivative. $$y=3 \cos 2 x$$

Differentiate. $$y=\log _{b} x^{3}$$

Integrate $$\int \tan 5 \theta d \theta$$

Exponential Functions $$\int 5^{7 x} d x$$

Find the average ordinate for each function in the given interval. $$y=\sqrt{1+2 x} \text { from } 4 \text { to } 12$$

Derivative of \(b^{u}\). Differentiate. $$y=(x)\left(10^{2 x+3}\right)$$

Find the derivative. $$y=\cos ^{-1} \frac{x}{a}$$

Find the derivative. $$y=5 \csc 3 x$$

First Derivatives Find the derivative. $$y=\cos ^{3} x$$

Differentiate. $$y=\log _{a}\left(x^{2}-3 x\right)$$

Integrate $$\int \sec 2 \theta d \theta$$

Exponential Functions $$\int 10^{x} d x$$

Find the average ordinate for each function in the given interval. $$y=\frac{x}{\sqrt{9+x^{2}}} \text { from } 0 \text { to } 4$$

Derivative of \(b^{u}\). Differentiate. $$y=10^{3 x}$$

Find the derivative. $$y=9 \cot 8 x$$

First Derivatives Find the derivative. $$y=\sin x^{2}$$

Integrate $$\int \sec 4 x \, d x$$

Differentiate. $$y=\log (x \sqrt{5+6 x})$$

Exponential Functions $$\int a^{3 y} d y$$

Find the average ordinate for each function in the given interval. $$y=\sin ^{2} x \quad \text { from } 0 \text { to } \pi / 2$$

Derivative of \(b^{u}\). Differentiate. $$y=2^{x^{2}}$$

Find the derivative. $$y=\sin ^{-1} \frac{\sin x-\cos x}{\sqrt{2}}$$

Find the derivative. $$y=3.25 \tan x^{2}$$

Integrate $$\int \cot 8 x \, d x$$

Differentiate. $$y=\log _{a}\left(\frac{1}{2 x+5}\right)$$

Find the average ordinate for each function in the given interval. $$2 y=\cos 2 x+1 \quad \text { from } 0 \text { to } \pi$$

Derivative of \(b^{u}\). Differentiate. $$y=7^{2 x}$$

Find the derivative. $$y=\sqrt{2 a x-x^{2}}+a \cos ^{-1} \frac{\sqrt{2 a x-x^{2}}}{a}$$

Find the derivative. $$y=5.14 \sec 2.11 x^{2}$$

First Derivatives Find the derivative. $$y=\cos 6 x$$

Integrate $$\int 3 \tan 9 \theta d \theta$$

Differentiate. $$y=x \log \frac{2}{x}$$

Exponential Functions $$\int 4 e^{x} d x$$

Find the rms value for each function in the given interval. \(y=2 x+1 \quad\) from 0 to 6.

Derivative of \(e^{u}\). Differentiate. $$y=e^{2 x}$$

First Derivatives Find the derivative. $$y=\sin x \cos x$$