∫ (from 2 to 6) of (3x+8) wrt x-এর সমাধান করুন

$$\int _ { 2 } ^ { 6 } ( 3 x + 8 ) d x$$

মূল্যায়ন করুন

$$80$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 3x+8\mathrm{d}x$$

Integrate the sum term by term.

$$\int 3x\mathrm{d}x+\int 8\mathrm{d}x$$

Factor out the constant in each of the terms.

$$3\int x\mathrm{d}x+\int 8\mathrm{d}x$$

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।

$$\frac{3x^{2}}{2}+\int 8\mathrm{d}x$$

Find the integral of 8 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{3x^{2}}{2}+8x$$

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.

$$\frac{3}{2}\times 6^{2}+8\times 6-\left(\frac{3}{2}\times 2^{2}+8\times 2\right)$$

সিমপ্লিফাই।

$$80$$