Resources

Resources

Find indefinite integrals using the substitution

h(n)=-91\cdot\left(-\frac{1}{7}\right)^{n-1}

\newline

Complete the recursive formula of

h(n)

\newline

h(1)=\square

\newline

h(n)=h(n-1) \cdot \square

Evaluate the integral:

\int \frac{-9}{\sqrt{36-16 x^{2}}} d x

Evaluate the integral:

\int \frac{2}{x \sqrt{x^{2}-36}} d x

Evaluate the integral:

\int \frac{-5}{36+4 x^{2}} d x

Given the function

f(x)=|x-3|

, what is the value of

\int_{2}^{5} f(x) d x

\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x

Use the long division method to find the result when

4 x^{3}+7 x^{2}-11 x-5

4 x-5

. If there is a remainder, express the result in the form

q(x)+\frac{r(x)}{b(x)}

C(2,-8),D(-6,4),E(0,4),U(1,-4),V(-3,2),

W(0,2)

\angle CDE

is the preimage of

\angle UVW

, represent the transformation algebraically.

\newline

(x,y)\mapsto(\square x,\square y)

C(2,-8),D(-6,4),E(0,4),U(1,-4),V(-3,2),

\newline

W(0,2)

\angle CDE

is the preimage of

\angle UVW

, represent the transformation algebraically.

\newline

(x,y)\rightarrow(\square x,\square y)

\left(x^{-12}\right)\left(x^{4}\right)

is equivalent to

x^{k}

. What is the value of

k

\newline

\newline

Rewrite the expression in the form

b^{n}

\newline

\frac{b^{-2}}{b^{4}}=\square

\int_{3}^{\infty}\frac{1}{x\sqrt{x^{2}-9}}dx

Evaluate the integral.

\newline

\int\frac{6\sec^{2}(3t)}{7+2\tan(3t)}\,dt

\int \frac{4y^{4}-y^{2}}{4y^{2}+1}\,dy

\int_{2}^{4}\frac{2}{x\sqrt{x^{2}-4}}dx

Use the graph of the integrand to evaluate the integral.

\newline

\int_{-1}^{1}(1+\sqrt{1-x^{2}})\,dx

\int \frac{\ln(x) + 5}{x} \, dx

\int \frac{dx}{4\sin^2(x)+8\sin(2x)-3\cos^2(x)}

\int x^{(x)}\,dx

\int \frac{x+2}{x^{3}+27}\,dx

\int\left(\frac{d}{dx}\left(\frac{1}{1+\log x}\right)\int 1 dx\right)dx

The volume of the solid obtained by rotating the region enclosed by

\newline

y=x^{2}, \quad x=y^{2}

\newline

x=-4

can be computed using the method of disks or washers via an integral

\newline

V=\int_{a}^{b}

\newline

\newline

with limits of integration

a=

b=

\newline

V=

\int \frac{5^{-x} d x}{\sqrt{5^{2} x+3 \cdot 5^{x}+1}}

\int \frac{5^{x} d x}{\sqrt{5^{2 x}+3 \cdot 5^{-x}+1}}

\int \frac{5^{x} d x}{\sqrt{5^{2 x}+3 \cdot 5^{x}+1}}

\int \frac{\cos x d x}{\sqrt{\sin ^{2} x+4 \sin x-1}}

9

2

\newline

Write in exponential notation:

\newline

\frac{a^{2}}{a^{8}}

Write in exponential notation:

\newline

\frac{w}{w^{4}}

Integration techniques: Evaluate

\int (x^2 + 3x - 2) \, dx

using appropriate integration methods.

x>0

, the expression

\sqrt[4]{x^{11}}

is equivalent to

\newline

x^{2} \sqrt[4]{x^{3}}

\newline

x^{2}

\newline

x^{3}

\newline

x^{2} \sqrt[4]{x^{2}}

x>0

, the expression

\sqrt{x^{4}}

is equivalent to

\newline

x^{2}

\newline

x \sqrt{x}

\newline

x^{2} \sqrt{x}

\newline

x

x>0

, the expression

\sqrt{x^{21}}

is equivalent to

\newline

x^{11} \sqrt{x}

\newline

x^{11} \sqrt{x^{2}}

\newline

x^{10} \sqrt{x}

\newline

x^{10} \sqrt{x^{2}}

x>0

, the expression

\sqrt{x^{8}}

is equivalent to

\newline

x^{4} \sqrt{x}

\newline

x^{5}

\newline

x^{5} \sqrt{x}

\newline

x^{4}

x>0

, the expression

\sqrt{x^{3}}

is equivalent to

\newline

x^{2}

\newline

x

\newline

x^{2} \sqrt{x^{2}}

\newline

x \sqrt{x}

Express in simplest radical form.

\newline

\sqrt{9 x^{13}}

\newline

\sqrt{9 x^{13}}

\newline

3 \sqrt{x^{13}}

\newline

x^{6} \sqrt{3 x}

\newline

3 x^{6} \sqrt{x}

x

y

are both positive, write the following expression in simplest radical form.

\newline

2 \sqrt{25 x^{6} y^{5}}

\newline

x

y

are both positive, write the following expression in simplest radical form.

\newline

8 y \sqrt{20 x^{2} y^{4}}

\newline

x

y

are both positive, write the following expression in simplest radical form.

\newline

6 \sqrt{54 x^{7} y^{2}}

\newline

x

y

are both positive, write the following expression in simplest radical form.

\newline

x^{2} \sqrt{75 x^{3} y^{6}}

\newline

Select the expression that is equivalent to

6 x^{\frac{1}{3}}

\newline

6 \sqrt{x^{3}}

\newline

\sqrt[3]{6 x}

\newline

6 \sqrt[3]{x}

\newline

\sqrt{6 x^{3}}

x>0

y>0

, select the expression that is equivalent to

\newline

\sqrt{-16 x^{8} y^{3}}

\newline

-4 x^{4} y^{\frac{3}{2}}

\newline

-4 x^{6} y

\newline

4 i x^{4} y^{\frac{3}{2}}

\newline

4 i x^{6} y

x>0

y>0

, select the expression that is equivalent to

\newline

\sqrt{-100 x^{7} y^{15}}

\newline

10 i x^{\frac{7}{2}} y^{\frac{15}{2}}

\newline

-10 x^{\frac{7}{2}} y^{\frac{15}{2}}

\newline

10 i x^{14} y^{30}

\newline

-10 x^{14} y^{30}

\int x d x+\int 2 d x

Solve the equation. Check your solution

\newline

19=2-(z+5)

\newline

Write in exponential notation:

\newline

\frac{w}{w^{4}}

Find the equation of the curve for which

y^{\prime \prime}=\frac{4}{x^{3}}

and which is tangent to the line

2 x+y=5

(1,3)

\int \frac{x}{\sqrt{9-4 x^{2}}} d x

Solve the equation using the multiplication property of equality:

\newline

\frac{2}{15} = -\frac{y}{5}

\newline

The solution set is __________.

13^{\text {th }}

term of the geometric sequence

1,-3,9, \ldots

\newline

10^{x}+11^{x}+12^{x}=13^{x}+14^{x} \\ x=\text { ?? }

...