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3 years ago

How would you do this question?

Mathematics

1 answer:

diamong [38]3 years ago

8 0

Answer:

1) ∫ x² e^(x) dx

4) ∫ x cos(x) dx

Step-by-step explanation:

To solve this problem, eliminate the choices that can be solved by substitution.

In the second problem, we can say u = x², and du = 2x dx.

∫ x cos(x²) dx = ∫ ½ cos(u) du

In the third problem, we can say u = x², and du = 2x dx.

∫ x e^(x²) dx = ∫ ½ e^(u) du

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Answer:

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Step-by-step explanation:

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3 years ago

What are the domain and range of x= -2?

nikdorinn [45]

Answer:

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Step-by-step explanation:

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3 years ago

Geometry math question no Guessing and Please show work thank you

KatRina [158]

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3 years ago

*Be sure to simplify fractions and rationalize denominators if necessary.

m_a_m_a [10]

As given by the question

There are given that the vector:

$\vec{v}=\vec{2i}+\vec{3j}$

Now,

From the formula to find the unit vector in same direction is:

$\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}$

Then,

$\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}$

Then,

$\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}$

Then,

Rationalize the denominator:

So,

$\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}$

Hence, the unit vector is shown below:

$\vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j$

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2 years ago