∫ (from 2 to 3) of (x^2+2x) wrt x=-এর সমাধান করুন

$$\int _ { 2 } ^ { 3 } ( x ^ { 2 } + 2 x ) d x =$$

মূল্যায়ন করুন

$$\frac{34}{3}\approx 11.333333333$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

Integrate the sum term by term.

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

Factor out the constant in each of the terms.

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

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}.

$$\frac{x^{3}}{3}+2\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. 2 কে \frac{x^{2}}{2} বার গুণ করুন।

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

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.

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

সিমপ্লিফাই।

$$\frac{34}{3}$$