Question

this is similar to section 4.2 problem 44: determine the indefinite integral. use capital c for the free constant.

$$ int 4 e ^ { 0.02 x } d x = $$

hint: follow example 8.

resources

ebook

Explanation:

Step1: Use the integral formula for \(e^{ax}\)

The integral formula is \(\int e^{ax}dx=\frac{1}{a}e^{ax}+C\) (\(a
eq0\)). For \(\int4e^{0.02x}dx\), we can factor out the constant \(4\) first. So \(\int4e^{0.02x}dx = 4\int e^{0.02x}dx\).

Step2: Apply the formula

Here \(a = 0.02\). Using \(\int e^{ax}dx=\frac{1}{a}e^{ax}+C\), we have \(4\times\frac{1}{0.02}e^{0.02x}+C\).

Step3: Simplify the coefficient

Calculate \(4\div0.02=\frac{4}{\frac{2}{100}}=\frac{4\times100}{2}=200\).

Answer:

\(200e^{0.02x}+C\)