∫ (from 0 to 5) of x^4-3x wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { 5 } x ^ { 4 } - 3 x d x$$

মূল্যায়ন করুন

$$\frac{1175}{2}=587.5$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int x^{4}-3x\mathrm{d}x$$

Integrate the sum term by term.

$$\int x^{4}\mathrm{d}x+\int -3x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x^{4}\mathrm{d}x-3\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}.

$$\frac{x^{5}}{5}-3\int x\mathrm{d}x$$

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}. -3 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{x^{5}}{5}-\frac{3x^{2}}{2}$$

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.

$$\frac{5^{5}}{5}-\frac{3}{2}\times 5^{2}-\left(\frac{0^{5}}{5}-\frac{3}{2}\times 0^{2}\right)$$

সিমপ্লিফাই।

$$\frac{1175}{2}$$