Solve ∫ (from 1 to 6) of 10x wrt x

$$\int_{ 1 }^{ 6 } 10x d x$$

Evaluate

$$175$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 10x\mathrm{d}x$$

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

$$10\int x\mathrm{d}x$$

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}. Multiply 10 times \frac{x^{2}}{2}.

$$5x^{2}$$

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.

$$5\times 6^{2}-5\times 1^{2}$$

Simplify.

$$175$$