Solve ∫ (from 0 to 1) of 1000*9.8*x*10 wrt x

$$\int _ { 0 } ^ { 1 } 1000 \times 9.8 \cdot x \cdot 10 d x$$

Evaluate

$$49000$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2\times 49\times 1000x\mathrm{d}x$$

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

$$2\times 49\times 1000\int x\mathrm{d}x$$

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}.

$$2\times 49\times 1000\times \frac{x^{2}}{2}$$

Simplify.

$$49000x^{2}$$

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.

$$49000\times 1^{2}-49000\times 0^{2}$$

Simplify.

$$49000$$