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

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

মূল্যায়ন করুন

$$18$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

Integrate the sum term by term.

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

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}.

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

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}.

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

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.

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

সিমপ্লিফাই।

$$18$$