Solve ∫ (from 0 to 0.06) of 28/0.12x wrt x

$$\int_{ 0 }^{ 0.06 } \frac{ 28 }{ 0.12 } x d x$$

Evaluate

$$0.42$$

Solution Steps

Expand \frac{28}{0.12} by multiplying both numerator and the denominator by 100.

$$\int _{0}^{0.06}\frac{2800}{12}x\mathrm{d}x$$

Reduce the fraction \frac{2800}{12} to lowest terms by extracting and canceling out 4.

$$\int _{0}^{0.06}\frac{700}{3}x\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{700x}{3}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{700\int x\mathrm{d}x}{3}$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.

$$\frac{350x^{2}}{3}$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\frac{350}{3}\times 0.06^{2}-\frac{350}{3}\times 0^{2}$$

Simplify.

$$\frac{21}{50}$$