∫ (from 2 to 4) of 1/sqrt{x wrt x-এর সমাধান করুন

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

মূল্যায়ন করুন

$$4-2\sqrt{2}\approx 1.171572875$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

x^{-\frac{1}{2}} হিসেবে \frac{1}{\sqrt{x}} পুনরায় লিখুন৷ Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{-\frac{1}{2}}\mathrm{d}x with \frac{x^{\frac{1}{2}}}{\frac{1}{2}}. Simplify and convert from exponential to radical form.

$$2\sqrt{x}$$

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.

$$2\times 4^{\frac{1}{2}}-2\times 2^{\frac{1}{2}}$$

সিমপ্লিফাই।

$$4-2\sqrt{2}$$