Solve ∫ (from Omega to - b) of sqrt{2}

$$\int _ { \Omega } ^ { - b } \sqrt { 2 }$$

Evaluate

$$-\sqrt{2}\left(b+\Omega \right)$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \sqrt{2}\mathrm{d}x$$

Find the integral of \sqrt{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{2}x$$

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.

$$2^{\frac{1}{2}}\left(-1\right)b-2^{\frac{1}{2}}\Omega$$

Simplify.

$$-\left(b+\Omega \right)\sqrt{2}$$

Differentiate w.r.t. Ω

$$-\sqrt{2}$$