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Answer the following True or False. $\newline$ Suppose $a$ and $b$ are both positive real numbers. Then $\int_{a}^{b}\frac{1}{x^{2}}dx=\int_{-b}^{-a}\frac{1}{x^{2}}dx.$ $\newline$ True $\newline$ False $\newline$ Next Question

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Properties of matrices

Full solution

Q. Answer the following True or False.

\newline

Suppose

a

and

b

are both positive real numbers. Then

\int_{a}^{b}\frac{1}{x^{2}}dx=\int_{-b}^{-a}\frac{1}{x^{2}}dx.

\newline

True

\newline

False

\newline

Next Question

Consider Integral Calculation: Let's consider the integral of $\frac{1}{x^2}$ from $a$ to $b$ . We know that the integral of $\frac{1}{x^2}$ with respect to $x$ is $-\frac{1}{x}$ . So, the integral from $a$ to $b$ of $\frac{1}{x^2} dx$ is $-\frac{1}{b} - \left(-\frac{1}{a}\right) = -\frac{1}{b} + \frac{1}{a}$ .
Calculate Integral from $a$ to $b$ : Now let's consider the integral of $\frac{1}{x^2}$ from $-b$ to $-a$ . Again, the integral of $\frac{1}{x^2}$ with respect to $x$ is $-\frac{1}{x}$ . So, the integral from $-b$ to $-a$ of $\frac{1}{x^2}$ $b$ $1$ is $b$ $2$ .
Calculate Integral from $-b$ to $-a$ : Comparing both results, we have from $a$ to $b$ : $-\frac{1}{b} + \frac{1}{a}$ , and from $-b$ to $-a$ : $\frac{1}{a} - \frac{1}{b}$ . These two results are not equal because one is the negative of the other. Therefore, the statement is false.

More problems from Properties of matrices

Question

Is this an identity matrix?

\newline

\begin{bmatrix} 0 & 1 1 & 0 \end{bmatrix}

\newline

\newline

\text{yes}

\newline

\text{no}

Posted 5 months ago

Question

Consider this matrix transformation:

\newline

\left[\begin{array}{ll} -3 & 4 \\ & \\ -3 & 2 \end{array}\right]

\newline

What is the image of

\left[\begin{array}{c}-2 \\ 2\end{array}\right]

under this transformation?

Posted 4 months ago

Question

Consider this matrix transformation:

\newline

\left[\begin{array}{cc} 2 & 3 \\ & \\ -3 & -1 \end{array}\right]

\newline

What is the image of

\left[\begin{array}{l}4 \\ 1\end{array}\right]

under this transformation?

Posted 9 months ago

Question

Consider this matrix transformation:

\newline

\left[\begin{array}{cc} -4 & -2 \\ 2 & 3 \end{array}\right]

\newline

What is the image of

\left[\begin{array}{c}3 \\ -1\end{array}\right]

under this transformation?

Posted 3 months ago

Question

Answer the following True or False.

\newline

\frac{d}{dx}3x^{\frac{1}{3}}=x^{-\frac{2}{3}}

, the fundamental theorem of calculus tells us that

\int_{-1}^{1}x^{-\frac{2}{3}}dx=3(1^{\frac{1}{3}})-3(-1)^{\frac{1}{3}}=6

\newline

\newline

Posted 8 months ago

Question

Answer the following True or False.

\newline

\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}

\newline

\newline

Posted 8 months ago

Question

Answer the following True or False.

\newline

\int \frac{1}{\sec x}\,dx = \ln(\sec x) + C

\newline

\newline

Posted 8 months ago

Question

Answer the following True or False.

\newline

\int_{-a}^{a}(3x^{3}+9x)dx=0

\newline

\newline

Posted 8 months ago

Question

x

makes the equation below true?

\newline

10 x+8=78

\newline

4

\newline

7

\newline

8

\newline

9

Posted 8 months ago

Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 1 month ago

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Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant