Solve ∫ (from 0 to 3) of 9800*x*30 wrt x

$$\int_{ 0 }^{ 3 } 9800 \times x \times 30 d x$$

Evaluate

$$1323000$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 30\times 9800x\mathrm{d}x$$

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

$$30\times 9800\int x\mathrm{d}x$$

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}.

$$30\times 9800\times \frac{x^{2}}{2}$$

Simplify.

$$147000x^{2}$$

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.

$$147000\times 3^{2}-147000\times 0^{2}$$

Simplify.

$$1323000$$