c ( 100 ) = ∫ (from 0 to 100) of (100+2x) wrt x-এর সমাধান করুন

$$c ( 100 ) = \int _ { 0 } ^ { 100 } ( 100 + 2 x ) d x$$

মূল্যায়ন করুন

$$20000$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 100+2x\mathrm{d}x$$

Integrate the sum term by term.

$$\int 100\mathrm{d}x+\int 2x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 100\mathrm{d}x+2\int x\mathrm{d}x$$

Find the integral of 100 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$100x+2\int x\mathrm{d}x$$

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}. 2 কে \frac{x^{2}}{2} বার গুণ করুন।

$$100x+x^{2}$$

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.

$$100\times 100+100^{2}-\left(100\times 0+0^{2}\right)$$

সিমপ্লিফাই।

$$20000$$