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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}

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Question

Consider this matrix transformation:

\newline

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

\newline

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Answer the following True or False.

\newline

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\newline

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Answer the following True or False.

\newline

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Answer the following True or False.

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Answer the following True or False.

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Question

x

makes the equation below true?

\newline

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\newline

4

\newline

7

\newline

8

\newline

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Question

Answer the following True or False. For all

1 < a < b

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\newline

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Question

Which expressions are equivalent to

z^{0.2}

\newline

Choose all answers that apply:

\newline

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\newline

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\newline

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\newline

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