Solve ∫ (from 1 to 2) of 2x^6 wrt x

$$\int _ { 1 } ^ { 2 } 2 x ^ { 6 } d x$$

Evaluate

$$\frac{254}{7}\approx 36.285714286$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 2x^{6}\mathrm{d}x$$

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

$$2\int x^{6}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{6}\mathrm{d}x with \frac{x^{7}}{7}.

$$\frac{2x^{7}}{7}$$

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.

$$\frac{2}{7}\times 2^{7}-\frac{2}{7}\times 1^{7}$$

Simplify.

$$\frac{254}{7}$$