Solve ∫ (from 373 to 800) of (30+10.7*10^-3) wrt x

$$\int _ { 373 } ^ { 800 } ( 30 + 10.7 \times 10 ^ { - 3 } ) d x$$

Evaluate

$$12814.5689$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\int _{373}^{800}30+10.7\times \frac{1}{1000}\mathrm{d}x$$

Multiply 10.7 and \frac{1}{1000} to get \frac{107}{10000}.

$$\int _{373}^{800}30+\frac{107}{10000}\mathrm{d}x$$

Add 30 and \frac{107}{10000} to get \frac{300107}{10000}.

$$\int _{373}^{800}\frac{300107}{10000}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{300107}{10000}\mathrm{d}x$$

Find the integral of \frac{300107}{10000} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{300107x}{10000}$$

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.

$$\frac{300107}{10000}\times 800-\frac{300107}{10000}\times 373$$

Simplify.

$$\frac{128145689}{10000}$$