Solve ∫ (from 0 to 1) of 1.124^x wrt x

$$\int_{ 0 }^{ 1 } { 1.124 }^{ x } d x$$

Evaluate

$$\frac{31}{250\ln(1.124)}\approx 1.060792373$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 1.124^{x}\mathrm{d}x$$

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

$$\frac{1.124^{x}}{\ln(1.124)}$$

Simplify.

$$\frac{1.124^{x}}{\ln(\frac{281}{250})}$$

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.

$$1.124^{1}\left(\ln(281)-\ln(250)\right)^{-1}-1.124^{0}\left(\ln(281)-\ln(250)\right)^{-1}$$

Simplify.

$$\frac{31}{250\ln(\frac{281}{250})}$$