∫ (from 0 to 6+3) of sqrt{x wrt x-এর সমাধান করুন

$$\int_{ 0 }^{ 6+3 } \sqrt{ x } d x$$

মূল্যায়ন করুন

$$18$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

x^{\frac{1}{2}} হিসেবে \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{3}{2}}}{\frac{3}{2}}. সিমপ্লিফাই।

$$\frac{2x^{\frac{3}{2}}}{3}$$

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.

$$\frac{2}{3}\left(6+3\right)^{\frac{3}{2}}-\frac{2}{3}\times 0^{\frac{3}{2}}$$

সিমপ্লিফাই।

$$18$$