Solve ∫ (from 0 to 2) of 5438x7/25x wrt x

$$\int_{ 0 }^{ 2 } 5438x \frac{ 7 }{ 25 } x d x$$

Evaluate

$$\frac{304528}{75}\approx 4060.373333333$$

Solution Steps

Multiply x and x to get x^{2}.

$$\int _{0}^{2}5438x^{2}\times \frac{7}{25}\mathrm{d}x$$

Express 5438\times \frac{7}{25} as a single fraction.

$$\int _{0}^{2}\frac{5438\times 7}{25}x^{2}\mathrm{d}x$$

Multiply 5438 and 7 to get 38066.

$$\int _{0}^{2}\frac{38066}{25}x^{2}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{38066x^{2}}{25}\mathrm{d}x$$

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

$$\frac{38066\int x^{2}\mathrm{d}x}{25}$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{38066x^{3}}{75}$$

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.

$$\frac{38066}{75}\times 2^{3}-\frac{38066}{75}\times 0^{3}$$

Simplify.

$$\frac{304528}{75}$$