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

$$\int_{ 0 }^{ 2 } 2 { x }^{ 2 } d x$$

মূল্যায়ন করুন

$$\frac{16}{3}\approx 5.333333333$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

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

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}.

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

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.

$$\frac{2}{3}\times 2^{3}-\frac{2}{3}\times 0^{3}$$

সিমপ্লিফাই।

$$\frac{16}{3}$$