Solve ∫ (from 1 to 2) of 4^x wrt x

$$\int _ { 1 } ^ { 2 } 4 ^ { x } d x$$

Evaluate

$$\frac{6}{\ln(2)}\approx 8.656170245$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 4^{x}\mathrm{d}x$$

Use \int x^{y}\mathrm{d}y=\frac{x^{y}}{\ln(x)} from the table of common integrals to obtain the result.

$$\frac{4^{x}}{\ln(4)}$$

Simplify.

$$\frac{4^{x}}{2\ln(2)}$$

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.

$$\frac{1}{2}\times 4^{2}\ln(2)^{-1}-\frac{1}{2}\times 4^{1}\ln(2)^{-1}$$

Simplify.

$$\frac{6}{\ln(2)}$$