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Chapter 17: Problem 2

Find \(\int 3 \mathrm{e}^{2 x} \mathrm{~d} x\).

Short Answer

Expert verified
Answer: The integral of the function \(3e^{2x}\) is \(\frac{3}{2}e^{2x} + C\).

Step by step solution

01

Identify the constants

Within the given integral, we have the constants \(a=3\) and \(b=2\).
02

Apply the integration rule

Apply the integration rule for an exponential function multiplied by a constant: \(\int ae^{bx} dx = \frac{a}{b}e^{bx} + C\). In this case, it will be \(\int 3e^{2x} dx = \frac{3}{2}e^{2x} + C\).
03

Write down the final answer

After applying the integration rule, the final answer is: \(\int 3e^{2x} dx = \frac{3}{2}e^{2x} + C\).

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Most popular questions from this chapter

Use Simpson's rule with the number of strips specified to approximate the following definite integrals: (a) \(\int_{0}^{0.8} \tan ^{2} x \mathrm{~d} x, 8\) strips (b) \(\int_{1}^{2} \sqrt{1+x^{3}} \mathrm{~d} x, 10\) strips

The mean square value of a function \(f(t)\) over the interval \(t=a\) to \(t=b\) is defined to be $$ \frac{1}{b-a} \int_{a}^{b}(f(t))^{2} \mathrm{~d} t $$ Find the mean square value of \(f(t)=\sin t\) over the interval \(t=0\) to \(t=2 \pi\).

Find \(\int \sin m t \sin n t \mathrm{~d} t\) where \(m\) and \(n\) are constants and \(m \neq n .\)

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Find \(\int \frac{\mathrm{d} x}{(1-x) \sqrt{x}}\).
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