∫ (from 3 to 7) of (5x-20) wrt x-এর সমাধান করুন

$$\int _ { 3 } ^ { 7 } ( 5 x - 20 ) d x$$

মূল্যায়ন করুন

$$20$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 5x-20\mathrm{d}x$$

Integrate the sum term by term.

$$\int 5x\mathrm{d}x+\int -20\mathrm{d}x$$

Factor out the constant in each of the terms.

$$5\int x\mathrm{d}x+\int -20\mathrm{d}x$$

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}. 5 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{5x^{2}}{2}+\int -20\mathrm{d}x$$

Find the integral of -20 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}-20x$$

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.

$$\frac{5}{2}\times 7^{2}-20\times 7-\left(\frac{5}{2}\times 3^{2}-20\times 3\right)$$

সিমপ্লিফাই।

$$20$$