Solve ∫ _{frac{-sqrt{2}-sqrt{6}}{4}}^sqrt{2/2 wrt x

$$\int _ { \frac { - \sqrt { 2 } - \sqrt { 6 } } { 4 } } ^ { \frac { \sqrt { 2 } } { 2 } } d x$$

Evaluate

$$\frac{\sqrt{6}+3\sqrt{2}}{4}\approx 1.673032607$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 1\mathrm{d}x$$

Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$x$$

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.

$$\frac{2^{\frac{1}{2}}}{2}-\frac{1}{4}\left(-2^{\frac{1}{2}}-6^{\frac{1}{2}}\right)$$

Simplify.

$$\frac{3\sqrt{2}+\sqrt{6}}{4}$$