∫ (from 1 to 2) of x^2/3.5 wrt x-এর সমাধান করুন

$$\int _ { 1 } ^ { 2 } \frac { x ^ { 2 } } { 3.5 } d x$$

মূল্যায়ন করুন

$$\frac{2}{3}\approx 0.666666667$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int \frac{2x^{2}}{7}\mathrm{d}x$$

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

$$\frac{2\int x^{2}\mathrm{d}x}{7}$$

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}.

$$\frac{2x^{3}}{21}$$

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.

$$\frac{2}{21}\times 2^{3}-\frac{2}{21}\times 1^{3}$$

সিমপ্লিফাই।

$$\frac{2}{3}$$