∫ (from 0 to 3) of (x+2) wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { 3 } ( x + 2 ) d x$$

মূল্যায়ন করুন

$$\frac{21}{2}=10.5$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

Integrate the sum term by term.

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

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}.

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

Find the integral of 2 using the table of common integrals rule \int a\mathrm{d}x=ax.

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

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.

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

সিমপ্লিফাই।

$$\frac{21}{2}$$