∫ (from x = 0 to 20) of x^2-এর সমাধান করুন

$$\int _ { x = 0 } ^ { 20 } x ^ { 2 }$$

মূল্যায়ন করুন

$$\frac{8000}{3}\approx 2666.666666667$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

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

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.

$$\frac{20^{3}}{3}-\frac{0^{3}}{3}$$

সিমপ্লিফাই।

$$\frac{8000}{3}$$