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german
4 years ago
15

Ex 4.8 14) integrate 3^(2x-1)

Mathematics
1 answer:
sesenic [268]4 years ago
4 0
Take the integral:

\large\begin{array}{l} \mathsf{\displaystyle\int\!3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\int\!\frac{1}{2}\cdot 2\cdot 3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^{2x-1}\cdot 2\,dx\qquad(i)} \end{array}


\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}


\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154165


\large\textsf{I hope it helps. :-)}
</span>

Tags: <em>integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

</em>
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Answer:

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Step-by-step explanation:

Data

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height = 250 in

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Process

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3.- Substitution

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4.- Simplification

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5.- Result

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the length of a rectangle is 4 meters less than twice its width. The area of the rectangle is 70. Find the dimensions of the rec
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70 = 2w² - 4w  reorganize to quadratic equation form

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w² - 2w - 35 = 0  factor this

(w - 7)(w + 5)    set each factor = 0 and calculate the value of w.

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Substitute into the original expressions to get the value of Length.

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Check by substituting into the original equation:

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