∫ (from 0 to 10) of 64x wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { 10 } 64 x d x$$

মূল্যায়ন করুন

$$3200$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 64x\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$64\int x\mathrm{d}x$$

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

$$32x^{2}$$

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.

$$32\times 10^{2}-32\times 0^{2}$$

সিমপ্লিফাই।

$$3200$$